%------------------------------------------------------------------------------
% File     : iProverMo---2.5-0.1
% Problem  : SCT171+6 : TPTP v8.1.0. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : iprover_modulo %s %d

% Computer : n027.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Mon Jul 18 21:38:56 EDT 2022

% Result   : Theorem 1.61s 1.80s
% Output   : CNFRefutation 1.69s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :  617
% Syntax   : Number of formulae    : 6589 (1072 unt;   0 def)
%            Number of atoms       : 22466 (5773 equ)
%            Maximal formula atoms :  152 (   3 avg)
%            Number of connectives : 26506 (10629   ~;13662   |; 481   &)
%                                         ( 240 <=>;1494  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   39 (   5 avg)
%            Maximal term depth    :   19 (   2 avg)
%            Number of predicates  :   30 (  28 usr;   1 prp; 0-2 aty)
%            Number of functors    :  271 ( 271 usr;  43 con; 0-6 aty)
%            Number of variables   : 19018 ( 516 sgn4998   !;  40   ?)

% Comments : 
%------------------------------------------------------------------------------
% Axioms transformation by autotheo
% Orienting (remaining) axiom formulas using strategy ClausalAll
% CNF of (remaining) axioms:
% Start CNF derivation
fof(c_0_0,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e))))))
  <=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))),lab)),lba)))) ),
    file('<stdin>',fact_81__096_Ic_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amk) ).

fof(c_0_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e))))))
  <=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),lab)),lba)))) ),
    file('<stdin>',fact_33__096_Ie_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amk) ).

fof(c_0_2,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,p)))
  <=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))))) ),
    file('<stdin>',fact_14_PW) ).

fof(c_0_3,axiom,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))))),
    file('<stdin>',fact_18__096e_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto) ).

fof(c_0_4,axiom,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))))),
    file('<stdin>',fact_17__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto) ).

fof(c_0_5,axiom,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))))),
    file('<stdin>',fact_13__096c_A_060_092_060_094bsub_062F_A_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amkto) ).

fof(c_0_6,axiom,
    hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))),arrow_1111136790e_Prof)),
    file('<stdin>',fact_16__096_I_Fi_O_Aif_Ah_Ai_A_060_An_Athen_Amktop_A_IP_Ai_J_Ae_Aelse_Aif_Ah_Ai) ).

fof(c_0_7,axiom,
    ~ ! [X44] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X44),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool)))))
       => ( ! [X32] :
              ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X32),X44))
             => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),X32))),lab)),lba)))) )
         => ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X44),one_one(nat))))),lab)),lba)))) ) ),
    file('<stdin>',fact_92__096_B_Bthesis_O_A_I_B_Bn_O_A_091_124_An_A_060_AN_059_AALL_Am_060_061n_O) ).

fof(c_0_8,axiom,
    ? [X44] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X44),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool)))))
      & ! [X32] :
          ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X32),X44))
         => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),X32))),lab)),lba)))) )
      & hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X44),one_one(nat))))),lab)),lba)))) ),
    file('<stdin>',fact_91__096EX_An_060N_O_A_IALL_Am_060_061n_O_Ab_A_060_092_060_094bsub_062F_A_I_) ).

fof(c_0_9,axiom,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))),lab)),lba)))),
    file('<stdin>',fact_80_n_I3_J) ).

fof(c_0_10,axiom,
    ! [X32] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X32),n))
     => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),X32))),lab)),lba)))) ),
    file('<stdin>',fact_45_n_I2_J) ).

fof(c_0_11,axiom,
    ! [X29] : hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),X29))),lab)),lba)),arrow_1111136790e_Prof)),
    file('<stdin>',fact_41_PiProf) ).

fof(c_0_12,axiom,
    ! [X3,X1,X41,X40] :
      ( hBOOL(hAPP(fun(X3,fun(X1,bool)),bool,hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,fun(X1,bool)),bool),ord_less_eq(fun(X3,fun(X1,bool))),hAPP(fun(product_prod(X3,X1),bool),fun(X3,fun(X1,bool)),hAPP(fun(X3,fun(fun(product_prod(X3,X1),bool),fun(X1,bool))),fun(fun(product_prod(X3,X1),bool),fun(X3,fun(X1,bool))),combc(X3,fun(product_prod(X3,X1),bool),fun(X1,bool)),hAPP(fun(X3,fun(X1,fun(fun(product_prod(X3,X1),bool),bool))),fun(X3,fun(fun(product_prod(X3,X1),bool),fun(X1,bool))),hAPP(fun(fun(X1,fun(fun(product_prod(X3,X1),bool),bool)),fun(fun(product_prod(X3,X1),bool),fun(X1,bool))),fun(fun(X3,fun(X1,fun(fun(product_prod(X3,X1),bool),bool))),fun(X3,fun(fun(product_prod(X3,X1),bool),fun(X1,bool)))),combb(fun(X1,fun(fun(product_prod(X3,X1),bool),bool)),fun(fun(product_prod(X3,X1),bool),fun(X1,bool)),X3),combc(X1,fun(product_prod(X3,X1),bool),bool)),hAPP(fun(X3,fun(X1,product_prod(X3,X1))),fun(X3,fun(X1,fun(fun(product_prod(X3,X1),bool),bool))),hAPP(fun(fun(X1,product_prod(X3,X1)),fun(X1,fun(fun(product_prod(X3,X1),bool),bool))),fun(fun(X3,fun(X1,product_prod(X3,X1))),fun(X3,fun(X1,fun(fun(product_prod(X3,X1),bool),bool)))),combb(fun(X1,product_prod(X3,X1)),fun(X1,fun(fun(product_prod(X3,X1),bool),bool)),X3),hAPP(fun(product_prod(X3,X1),fun(fun(product_prod(X3,X1),bool),bool)),fun(fun(X1,product_prod(X3,X1)),fun(X1,fun(fun(product_prod(X3,X1),bool),bool))),combb(product_prod(X3,X1),fun(fun(product_prod(X3,X1),bool),bool),X1),member(product_prod(X3,X1)))),product_Pair(X3,X1)))),X41)),hAPP(fun(product_prod(X3,X1),bool),fun(X3,fun(X1,bool)),hAPP(fun(X3,fun(fun(product_prod(X3,X1),bool),fun(X1,bool))),fun(fun(product_prod(X3,X1),bool),fun(X3,fun(X1,bool))),combc(X3,fun(product_prod(X3,X1),bool),fun(X1,bool)),hAPP(fun(X3,fun(X1,fun(fun(product_prod(X3,X1),bool),bool))),fun(X3,fun(fun(product_prod(X3,X1),bool),fun(X1,bool))),hAPP(fun(fun(X1,fun(fun(product_prod(X3,X1),bool),bool)),fun(fun(product_prod(X3,X1),bool),fun(X1,bool))),fun(fun(X3,fun(X1,fun(fun(product_prod(X3,X1),bool),bool))),fun(X3,fun(fun(product_prod(X3,X1),bool),fun(X1,bool)))),combb(fun(X1,fun(fun(product_prod(X3,X1),bool),bool)),fun(fun(product_prod(X3,X1),bool),fun(X1,bool)),X3),combc(X1,fun(product_prod(X3,X1),bool),bool)),hAPP(fun(X3,fun(X1,product_prod(X3,X1))),fun(X3,fun(X1,fun(fun(product_prod(X3,X1),bool),bool))),hAPP(fun(fun(X1,product_prod(X3,X1)),fun(X1,fun(fun(product_prod(X3,X1),bool),bool))),fun(fun(X3,fun(X1,product_prod(X3,X1))),fun(X3,fun(X1,fun(fun(product_prod(X3,X1),bool),bool)))),combb(fun(X1,product_prod(X3,X1)),fun(X1,fun(fun(product_prod(X3,X1),bool),bool)),X3),hAPP(fun(product_prod(X3,X1),fun(fun(product_prod(X3,X1),bool),bool)),fun(fun(X1,product_prod(X3,X1)),fun(X1,fun(fun(product_prod(X3,X1),bool),bool))),combb(product_prod(X3,X1),fun(fun(product_prod(X3,X1),bool),bool),X1),member(product_prod(X3,X1)))),product_Pair(X3,X1)))),X40)))
    <=> hBOOL(hAPP(fun(product_prod(X3,X1),bool),bool,hAPP(fun(product_prod(X3,X1),bool),fun(fun(product_prod(X3,X1),bool),bool),ord_less_eq(fun(product_prod(X3,X1),bool)),X41),X40)) ),
    file('<stdin>',fact_157_pred__subset__eq2) ).

fof(c_0_13,axiom,
    ! [X42,X71] :
      ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),X71))
     => hAPP(nat,nat,suc,hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),hAPP(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool)),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool))),combb(nat,fun(fun(nat,bool),bool),nat),member(nat)),suc)),X71))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X42))))) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),X71))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,X42))))) ),
    file('<stdin>',fact_433_card__less__Suc) ).

fof(c_0_14,axiom,
    ! [X42,X71] :
      ( ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),X71))
     => hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),hAPP(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool)),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool))),combb(nat,fun(fun(nat,bool),bool),nat),member(nat)),suc)),X71))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X42)))) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),X71))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,X42))))) ),
    file('<stdin>',fact_435_card__less__Suc2) ).

fof(c_0_15,axiom,
    ! [X3,X1] :
      ( ( order(X1)
        & order(X3) )
     => ! [X37,X17,X14,X15] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X14),X15))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X3,X1,X37,X15)),X17))
           => ( ! [X26,X46] :
                  ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X26),X46))
                 => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X3,X1,X37,X26)),hAPP(X3,X1,X37,X46))) )
             => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X3,X1,X37,X14)),X17)) ) ) ) ),
    file('<stdin>',fact_216_order__less__le__subst2) ).

fof(c_0_16,axiom,
    ! [X3,X1] :
      ( ( order(X1)
        & order(X3) )
     => ! [X37,X17,X14,X15] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X14),X15))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X3,X1,X37,X15)),X17))
           => ( ! [X26,X46] :
                  ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X26),X46))
                 => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X3,X1,X37,X26)),hAPP(X3,X1,X37,X46))) )
             => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X3,X1,X37,X14)),X17)) ) ) ) ),
    file('<stdin>',fact_187_order__le__less__subst2) ).

fof(c_0_17,axiom,
    ! [X1,X3] :
      ( ( order(X3)
        & order(X1) )
     => ! [X17,X37,X15,X14] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X1,X3,X37,X15)),X14))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X17),X15))
           => ( ! [X26,X46] :
                  ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X46),X26))
                 => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X1,X3,X37,X46)),hAPP(X1,X3,X37,X26))) )
             => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X1,X3,X37,X17)),X14)) ) ) ) ),
    file('<stdin>',fact_184_xt4) ).

fof(c_0_18,axiom,
    ! [X1,X3] :
      ( ( order(X3)
        & ord(X1) )
     => ! [X17,X37,X15,X14] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X1,X3,X37,X15)),X14))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X17),X15))
           => ( ! [X26,X46] :
                  ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X46),X26))
                 => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X1,X3,X37,X46)),hAPP(X1,X3,X37,X26))) )
             => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X1,X3,X37,X17)),X14)) ) ) ) ),
    file('<stdin>',fact_183_xt6) ).

fof(c_0_19,axiom,
    ! [X1,X3] :
      ( ( order(X3)
        & order(X1) )
     => ! [X17,X37,X15,X14] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X15),X14))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X17),hAPP(X3,X1,X37,X15)))
           => ( ! [X26,X46] :
                  ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X46),X26))
                 => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X3,X1,X37,X46)),hAPP(X3,X1,X37,X26))) )
             => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X17),hAPP(X3,X1,X37,X14))) ) ) ) ),
    file('<stdin>',fact_213_xt7) ).

fof(c_0_20,axiom,
    ! [X1,X3] :
      ( ( order(X3)
        & order(X1) )
     => ! [X17,X37,X15,X14] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X15),X14))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X17),hAPP(X3,X1,X37,X15)))
           => ( ! [X26,X46] :
                  ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X46),X26))
                 => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X3,X1,X37,X46)),hAPP(X3,X1,X37,X26))) )
             => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X17),hAPP(X3,X1,X37,X14))) ) ) ) ),
    file('<stdin>',fact_212_xt5) ).

fof(c_0_21,axiom,
    ! [X3,X1] :
      ( ( order(X1)
        & order(X3) )
     => ! [X17,X14,X37,X15] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X14),hAPP(X1,X3,X37,X15)))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X15),X17))
           => ( ! [X26,X46] :
                  ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X26),X46))
                 => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X1,X3,X37,X26)),hAPP(X1,X3,X37,X46))) )
             => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X14),hAPP(X1,X3,X37,X17))) ) ) ) ),
    file('<stdin>',fact_186_order__less__le__subst1) ).

fof(c_0_22,axiom,
    ! [X3,X1] :
      ( ( order(X1)
        & order(X3) )
     => ! [X17,X14,X37,X15] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X14),hAPP(X1,X3,X37,X15)))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X15),X17))
           => ( ! [X26,X46] :
                  ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X26),X46))
                 => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X1,X3,X37,X26)),hAPP(X1,X3,X37,X46))) )
             => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X14),hAPP(X1,X3,X37,X17))) ) ) ) ),
    file('<stdin>',fact_185_order__le__less__subst1) ).

fof(c_0_23,axiom,
    ! [X10,X11,X12,X13,X14,X15] :
      ( ti(arrow_490897120le_alt,X14) != ti(arrow_490897120le_alt,X15)
     => ( ti(arrow_490897120le_alt,X12) != ti(arrow_490897120le_alt,X13)
       => ( ti(arrow_490897120le_alt,X14) != ti(arrow_490897120le_alt,X13)
         => ( ti(arrow_490897120le_alt,X15) != ti(arrow_490897120le_alt,X12)
           => ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X11),arrow_1111136790e_Prof))
             => ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X10),arrow_1111136790e_Prof))
               => ( ! [X16] :
                      ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X14),X15)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X11,X16)))
                    <=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X12),X13)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X10,X16))) )
                 => ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X14),X15)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X11)))
                   => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X12),X13)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X10))) ) ) ) ) ) ) ) ),
    file('<stdin>',fact_7__C1_C) ).

fof(c_0_24,axiom,
    ! [X10,X11,X12,X13,X14,X15] :
      ( ti(arrow_490897120le_alt,X14) != ti(arrow_490897120le_alt,X15)
     => ( ti(arrow_490897120le_alt,X12) != ti(arrow_490897120le_alt,X13)
       => ( ti(arrow_490897120le_alt,X14) != ti(arrow_490897120le_alt,X13)
         => ( ti(arrow_490897120le_alt,X15) != ti(arrow_490897120le_alt,X12)
           => ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X11),arrow_1111136790e_Prof))
             => ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X10),arrow_1111136790e_Prof))
               => ( ! [X16] :
                      ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X14),X15)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X11,X16)))
                    <=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X12),X13)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X10,X16))) )
                 => ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X14),X15)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X11)))
                  <=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X12),X13)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X10))) ) ) ) ) ) ) ) ),
    file('<stdin>',fact_6__C2_C) ).

fof(c_0_25,axiom,
    ! [X10,X11,X12,X13,X14,X15] :
      ( ti(arrow_490897120le_alt,X14) != ti(arrow_490897120le_alt,X15)
     => ( ti(arrow_490897120le_alt,X12) != ti(arrow_490897120le_alt,X13)
       => ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X11),arrow_1111136790e_Prof))
         => ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X10),arrow_1111136790e_Prof))
           => ( ! [X16] :
                  ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X14),X15)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X11,X16)))
                <=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X12),X13)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X10,X16))) )
             => ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X14),X15)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X11)))
              <=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X12),X13)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X10))) ) ) ) ) ) ),
    file('<stdin>',fact_9_pairwise__neutrality) ).

fof(c_0_26,axiom,
    ! [X42,X71] :
      ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),X71))
     => hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),X71))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,X42))))) != zero_zero(nat) ),
    file('<stdin>',fact_434_card__less) ).

fof(c_0_27,axiom,
    ! [X16] :
      ( ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X16)),n))
         => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X16)),e))) )
        & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X16)),n))
         => ( ( hAPP(arrow_660593299e_indi,nat,h,X16) = n
             => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X16)),c),e))) )
            & ( hAPP(arrow_660593299e_indi,nat,h,X16) != n
             => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X16)),e))) ) ) ) )
    <=> ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X16)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
         => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab)) )
        & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X16)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
         => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba)) ) ) ),
    file('<stdin>',fact_82__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amk) ).

fof(c_0_28,axiom,
    ! [X42,X25] :
      ( hBOOL(hAPP(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X25),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1111136790e_Prof),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_2064824852le_Lin))))
     => ( ! [X26] :
            ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X26),arrow_1111136790e_Prof))
           => ! [X19,X20] :
                ( ti(arrow_490897120le_alt,X19) != ti(arrow_490897120le_alt,X20)
               => ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X19),X20)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X26,X42)))
                 => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X19),X20)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X25,X26))) ) ) )
       => hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,X25),X42)) ) ),
    file('<stdin>',fact_85_dictatorI) ).

fof(c_0_29,axiom,
    ! [X16] :
      ( ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X16)),n))
         => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X16)),e))) )
        & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X16)),n))
         => ( ( hAPP(arrow_660593299e_indi,nat,h,X16) = n
             => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X16)),c),e))) )
            & ( hAPP(arrow_660593299e_indi,nat,h,X16) != n
             => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X16)),e))) ) ) ) )
    <=> ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X16)),n))
         => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab)) )
        & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X16)),n))
         => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba)) ) ) ),
    file('<stdin>',fact_44__096ALL_Ai_O_A_Ie_A_060_092_060_094bsub_062_Iif_Ah_Ai_A_060_An_Athen_Amk) ).

fof(c_0_30,axiom,
    ! [X16] :
      ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X16)))
    <=> ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X16)),n))
         => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X16)),e))) )
        & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X16)),n))
         => ( ( hAPP(arrow_660593299e_indi,nat,h,X16) = n
             => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X16)),c),e))) )
            & ( hAPP(arrow_660593299e_indi,nat,h,X16) != n
             => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X16)),e))) ) ) ) ) ),
    file('<stdin>',fact_11__096ALL_Ai_O_A_Ic_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ad_J) ).

fof(c_0_31,axiom,
    ! [X25] :
      ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X25))
    <=> ! [X26] :
          ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X26),arrow_1111136790e_Prof))
         => ! [X27] :
              ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X27),arrow_1111136790e_Prof))
             => ! [X19,X20] :
                  ( ! [X16] :
                      ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X19),X20)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X26,X16)))
                    <=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X19),X20)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X27,X16))) )
                 => ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X19),X20)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X25,X26)))
                  <=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X19),X20)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X25,X27))) ) ) ) ) ),
    file('<stdin>',fact_23_IIA__def) ).

fof(c_0_32,axiom,
    ! [X10,X11,X17,X14,X15] :
      ( ti(arrow_490897120le_alt,X14) != ti(arrow_490897120le_alt,X15)
     => ( ti(arrow_490897120le_alt,X15) != ti(arrow_490897120le_alt,X17)
       => ( ti(arrow_490897120le_alt,X14) != ti(arrow_490897120le_alt,X17)
         => ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X11),arrow_1111136790e_Prof))
           => ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X10),arrow_1111136790e_Prof))
             => ( ! [X16] :
                    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X14),X15)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X11,X16)))
                  <=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X15),X17)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X10,X16))) )
               => ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X14),X15)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X11)))
                <=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X15),X17)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X10))) ) ) ) ) ) ) ),
    file('<stdin>',fact_8__C4_C) ).

fof(c_0_33,axiom,
    ! [X3,X11,X50] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),hAPP(fun(X3,bool),fun(X3,bool),collect(X3),hAPP(fun(X3,bool),fun(X3,bool),hAPP(fun(X3,fun(bool,bool)),fun(fun(X3,bool),fun(X3,bool)),combs(X3,bool,bool),hAPP(fun(X3,bool),fun(X3,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X3,bool),fun(X3,fun(bool,bool))),combb(bool,fun(bool,bool),X3),fdisj),X11)),X50))))
    <=> ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),hAPP(fun(X3,bool),fun(X3,bool),collect(X3),X11)))
        & hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),hAPP(fun(X3,bool),fun(X3,bool),collect(X3),X50))) ) ),
    file('<stdin>',fact_289_finite__Collect__disjI) ).

fof(c_0_34,axiom,
    ! [X10,X11,X14,X15] :
      ( ti(arrow_490897120le_alt,X14) != ti(arrow_490897120le_alt,X15)
     => ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X11),arrow_1111136790e_Prof))
       => ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X10),arrow_1111136790e_Prof))
         => ( ! [X16] :
                ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X14),X15)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X11,X16)))
              <=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X15),X14)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X10,X16))) )
           => ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X14),X15)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X11)))
            <=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X15),X14)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X10))) ) ) ) ) ),
    file('<stdin>',fact_10__C3_C) ).

fof(c_0_35,axiom,
    ! [X11,X42] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),X11)),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X42))))),
    file('<stdin>',fact_312_finite__M__bounded__by__nat) ).

fof(c_0_36,axiom,
    ! [X6,X7,X8,X14,X15] :
      ( ti(arrow_490897120le_alt,X14) != ti(arrow_490897120le_alt,X15)
     => ( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X8),arrow_2064824852le_Lin))
       => ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X6),X7)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X8),X14),X15)))
        <=> ( ti(arrow_490897120le_alt,X6) != ti(arrow_490897120le_alt,X7)
            & ( ti(arrow_490897120le_alt,X7) = ti(arrow_490897120le_alt,X14)
             => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X6),X15)),X8)) )
            & ( ti(arrow_490897120le_alt,X7) != ti(arrow_490897120le_alt,X14)
             => ( ( ti(arrow_490897120le_alt,X6) = ti(arrow_490897120le_alt,X14)
                 => ( ti(arrow_490897120le_alt,X7) = ti(arrow_490897120le_alt,X15)
                    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X15),X7)),X8)) ) )
                & ( ti(arrow_490897120le_alt,X6) != ti(arrow_490897120le_alt,X14)
                 => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X6),X7)),X8)) ) ) ) ) ) ) ),
    file('<stdin>',fact_217_in__below) ).

fof(c_0_37,axiom,
    ! [X6,X7,X8,X14,X15] :
      ( ti(arrow_490897120le_alt,X14) != ti(arrow_490897120le_alt,X15)
     => ( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X8),arrow_2064824852le_Lin))
       => ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X6),X7)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X8),X14),X15)))
        <=> ( ti(arrow_490897120le_alt,X6) != ti(arrow_490897120le_alt,X7)
            & ( ti(arrow_490897120le_alt,X6) = ti(arrow_490897120le_alt,X15)
             => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X14),X7)),X8)) )
            & ( ti(arrow_490897120le_alt,X6) != ti(arrow_490897120le_alt,X15)
             => ( ( ti(arrow_490897120le_alt,X7) = ti(arrow_490897120le_alt,X15)
                 => ( ti(arrow_490897120le_alt,X6) = ti(arrow_490897120le_alt,X14)
                    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X6),X14)),X8)) ) )
                & ( ti(arrow_490897120le_alt,X7) != ti(arrow_490897120le_alt,X15)
                 => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X6),X7)),X8)) ) ) ) ) ) ) ),
    file('<stdin>',fact_78_in__above) ).

fof(c_0_38,axiom,
    ! [X1,X3,X43,X49,X39] :
      ( ! [X26] :
          ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X26),X39))
         => hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(X3,fun(X1,bool),X43,X26)),hAPP(X3,fun(X1,bool),X49,X26))) )
     => hBOOL(hAPP(fun(fun(X3,X1),bool),bool,hAPP(fun(fun(X3,X1),bool),fun(fun(fun(X3,X1),bool),bool),ord_less_eq(fun(fun(X3,X1),bool)),hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool)),pi(X3,X1),X39),X43)),hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool)),pi(X3,X1),X39),X49))) ),
    file('<stdin>',fact_210_Pi__mono) ).

fof(c_0_39,axiom,
    ! [X1,X3,X43,X37,X38,X39] :
      ( ! [X47] :
          ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X47),X39))
         => hAPP(X3,X1,X37,X47) = hAPP(X3,X1,X38,X47) )
     => ( hBOOL(hAPP(fun(fun(X3,X1),bool),bool,hAPP(fun(X3,X1),fun(fun(fun(X3,X1),bool),bool),member(fun(X3,X1)),X37),hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool)),pi(X3,X1),X39),X43)))
      <=> hBOOL(hAPP(fun(fun(X3,X1),bool),bool,hAPP(fun(X3,X1),fun(fun(fun(X3,X1),bool),bool),member(fun(X3,X1)),X38),hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool)),pi(X3,X1),X39),X43))) ) ),
    file('<stdin>',fact_272_Pi__cong) ).

fof(c_0_40,axiom,
    ! [X3,X1,X40,X41] :
      ( ! [X26,X27] :
          ( hBOOL(hAPP(fun(product_prod(X3,X1),bool),bool,hAPP(product_prod(X3,X1),fun(fun(product_prod(X3,X1),bool),bool),member(product_prod(X3,X1)),hAPP(X1,product_prod(X3,X1),hAPP(X3,fun(X1,product_prod(X3,X1)),product_Pair(X3,X1),X26),X27)),X41))
        <=> hBOOL(hAPP(fun(product_prod(X3,X1),bool),bool,hAPP(product_prod(X3,X1),fun(fun(product_prod(X3,X1),bool),bool),member(product_prod(X3,X1)),hAPP(X1,product_prod(X3,X1),hAPP(X3,fun(X1,product_prod(X3,X1)),product_Pair(X3,X1),X26),X27)),X40)) )
    <=> ti(fun(product_prod(X3,X1),bool),X41) = ti(fun(product_prod(X3,X1),bool),X40) ),
    file('<stdin>',fact_79_pred__equals__eq2) ).

fof(c_0_41,axiom,
    hBOOL(hAPP(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),f),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1111136790e_Prof),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_2064824852le_Lin)))),
    file('<stdin>',fact_32_assms_I1_J) ).

fof(c_0_42,axiom,
    ! [X3,X50,X11] :
      ( ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),hAPP(fun(X3,bool),fun(X3,bool),collect(X3),X11)))
        | hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),hAPP(fun(X3,bool),fun(X3,bool),collect(X3),X50))) )
     => hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),hAPP(fun(X3,bool),fun(X3,bool),collect(X3),hAPP(fun(X3,bool),fun(X3,bool),hAPP(fun(X3,fun(bool,bool)),fun(fun(X3,bool),fun(X3,bool)),combs(X3,bool,bool),hAPP(fun(X3,bool),fun(X3,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X3,bool),fun(X3,fun(bool,bool))),combb(bool,fun(bool,bool),X3),fconj),X11)),X50)))) ),
    file('<stdin>',fact_283_finite__Collect__conjI) ).

fof(c_0_43,axiom,
    ! [X66,X37] :
      ( ! [X44] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X44),hAPP(nat,nat,X37,X44)))
     => hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less_eq(nat)),X37)),X66)))) ),
    file('<stdin>',fact_315_finite__less__ub) ).

fof(c_0_44,axiom,
    ! [X1,X3,X37,X43,X39] :
      ( ! [X26] :
          ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X26),X39))
         => hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X3,X1,X37,X26)),hAPP(X3,fun(X1,bool),X43,X26))) )
     => hBOOL(hAPP(fun(fun(X3,X1),bool),bool,hAPP(fun(X3,X1),fun(fun(fun(X3,X1),bool),bool),member(fun(X3,X1)),X37),hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool)),pi(X3,X1),X39),X43))) ),
    file('<stdin>',fact_273_Pi__I_H) ).

fof(c_0_45,axiom,
    ! [X1,X3,X37,X43,X39] :
      ( ! [X26] :
          ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X26),X39))
         => hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X3,X1,X37,X26)),hAPP(X3,fun(X1,bool),X43,X26))) )
     => hBOOL(hAPP(fun(fun(X3,X1),bool),bool,hAPP(fun(X3,X1),fun(fun(fun(X3,X1),bool),bool),member(fun(X3,X1)),X37),hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool)),pi(X3,X1),X39),X43))) ),
    file('<stdin>',fact_147_Pi__I) ).

fof(c_0_46,axiom,
    ! [X3] :
      ( linordered_idom(X3)
     => ! [X14] :
          ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X14),ring_1_Ints(X3)))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),one_one(X3)),X14)),X14)),zero_zero(X3)))
          <=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X14),zero_zero(X3))) ) ) ),
    file('<stdin>',fact_457_Ints__odd__less__0) ).

fof(c_0_47,axiom,
    ! [X1,X3,X43,X39,X37,X9,X38,X25] :
      ( hBOOL(hAPP(fun(fun(X1,bool),X3),bool,hAPP(fun(X1,X3),fun(fun(fun(X1,bool),X3),bool),hAPP(X3,fun(fun(X1,X3),fun(fun(fun(X1,bool),X3),bool)),hAPP(fun(X3,fun(X3,X3)),fun(X3,fun(fun(X1,X3),fun(fun(fun(X1,bool),X3),bool))),finite908156982e_idem(X3,X1),X37),X9),X38),X25))
     => ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X39))
       => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X43),X39))
         => hAPP(X3,X3,hAPP(X3,fun(X3,X3),X37,hAPP(fun(X1,bool),X3,X25,X43)),hAPP(fun(X1,bool),X3,X25,X39)) = hAPP(fun(X1,bool),X3,X25,X39) ) ) ),
    file('<stdin>',fact_303_folding__image__simple__idem_Osubset__idem) ).

fof(c_0_48,axiom,
    ! [X1,X3,X37,X43,X39] :
      ( ! [X26] :
          ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X26),X39))
         => hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X3,X1,X37,X26)),X43)) )
     => hBOOL(hAPP(fun(fun(X3,X1),bool),bool,hAPP(fun(X3,X1),fun(fun(fun(X3,X1),bool),bool),member(fun(X3,X1)),X37),hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool)),pi(X3,X1),X39),hAPP(fun(X1,bool),fun(X3,fun(X1,bool)),combk(fun(X1,bool),X3),X43)))) ),
    file('<stdin>',fact_270_funcsetI) ).

fof(c_0_49,axiom,
    ! [X1,X3,X6,X39,X37,X9,X38,X25] :
      ( hBOOL(hAPP(fun(fun(X1,bool),X3),bool,hAPP(fun(X1,X3),fun(fun(fun(X1,bool),X3),bool),hAPP(X3,fun(fun(X1,X3),fun(fun(fun(X1,bool),X3),bool)),hAPP(fun(X3,fun(X3,X3)),fun(X3,fun(fun(X1,X3),fun(fun(fun(X1,bool),X3),bool))),finite908156982e_idem(X3,X1),X37),X9),X38),X25))
     => ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X39))
       => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X39))
         => hAPP(X3,X3,hAPP(X3,fun(X3,X3),X37,hAPP(X1,X3,X38,X6)),hAPP(fun(X1,bool),X3,X25,X39)) = hAPP(fun(X1,bool),X3,X25,X39) ) ) ),
    file('<stdin>',fact_310_folding__image__simple__idem_Oin__idem) ).

fof(c_0_50,axiom,
    ! [X3,X1,X38,X37,X39,X43] :
      ( hBOOL(hAPP(fun(fun(X3,X1),bool),bool,hAPP(fun(X3,X1),fun(fun(fun(X3,X1),bool),bool),member(fun(X3,X1)),X37),hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool)),pi(X3,X1),X39),hAPP(fun(X1,bool),fun(X3,fun(X1,bool)),combk(fun(X1,bool),X3),X43))))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),X39))
       => ( hBOOL(hAPP(fun(fun(X1,X3),bool),bool,hAPP(fun(X1,X3),fun(fun(fun(X1,X3),bool),bool),member(fun(X1,X3)),X38),hAPP(fun(X1,fun(X3,bool)),fun(fun(X1,X3),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X3,bool)),fun(fun(X1,X3),bool)),pi(X1,X3),X43),hAPP(fun(X3,bool),fun(X1,fun(X3,bool)),combk(fun(X3,bool),X1),X39))))
         => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X38),X43))
           => ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39))
             => ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43))
               => hAPP(fun(X3,bool),nat,finite_card(X3),X39) = hAPP(fun(X1,bool),nat,finite_card(X1),X43) ) ) ) ) ) ),
    file('<stdin>',fact_278_card__bij) ).

fof(c_0_51,axiom,
    ! [X25] :
      ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,X25))
    <=> ! [X26] :
          ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X26),arrow_1111136790e_Prof))
         => ! [X19,X20] :
              ( ! [X16] : hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X19),X20)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X26,X16)))
             => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X19),X20)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X25,X26))) ) ) ),
    file('<stdin>',fact_24_unanimity__def) ).

fof(c_0_52,axiom,
    ! [X1,X3,X6,X37,X9,X38,X25] :
      ( hBOOL(hAPP(fun(fun(X1,bool),X3),bool,hAPP(fun(X1,X3),fun(fun(fun(X1,bool),X3),bool),hAPP(X3,fun(fun(X1,X3),fun(fun(fun(X1,bool),X3),bool)),hAPP(fun(X3,fun(X3,X3)),fun(X3,fun(fun(X1,X3),fun(fun(fun(X1,bool),X3),bool))),finite908156982e_idem(X3,X1),X37),X9),X38),X25))
     => hAPP(X3,X3,hAPP(X3,fun(X3,X3),X37,X6),X6) = ti(X3,X6) ),
    file('<stdin>',fact_305_folding__image__simple__idem_Oidem) ).

fof(c_0_53,axiom,
    ! [X3,X1,X37,X39] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X3,bool),nat,finite_card(X3),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X37),X39))),hAPP(fun(X1,bool),nat,finite_card(X1),X39)))
     => ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X37),X39)) ),
    file('<stdin>',fact_472_pigeonhole) ).

fof(c_0_54,axiom,
    ! [X8,X6,X7] :
      ( ti(arrow_490897120le_alt,X6) != ti(arrow_490897120le_alt,X7)
     => ( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X8),arrow_2064824852le_Lin))
       => hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X8),X6),X7)),arrow_2064824852le_Lin)) ) ),
    file('<stdin>',fact_238_below__Lin) ).

fof(c_0_55,axiom,
    ! [X8,X6,X7] :
      ( ti(arrow_490897120le_alt,X6) != ti(arrow_490897120le_alt,X7)
     => ( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X8),arrow_2064824852le_Lin))
       => hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X8),X6),X7)),arrow_2064824852le_Lin)) ) ),
    file('<stdin>',fact_50_above__Lin) ).

fof(c_0_56,axiom,
    ! [X6,X7,X8] :
      ( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X8),arrow_2064824852le_Lin))
     => ( ti(arrow_490897120le_alt,X6) != ti(arrow_490897120le_alt,X7)
       => ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X6),X7)),X8))
        <=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X7),X6)),X8)) ) ) ),
    file('<stdin>',fact_46_notin__Lin__iff) ).

fof(c_0_57,axiom,
    ! [X14,X15,X8] :
      ( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X8),arrow_2064824852le_Lin))
     => ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X14),X15)),X8))
       => ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X15),X14)),X8)) ) ),
    file('<stdin>',fact_47_Lin__irrefl) ).

fof(c_0_58,axiom,
    ! [X3,X41,X40] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),hAPP(fun(X3,bool),fun(X3,bool),hAPP(fun(X3,fun(fun(X3,bool),bool)),fun(fun(X3,bool),fun(X3,bool)),combc(X3,fun(X3,bool),bool),member(X3)),X41)),hAPP(fun(X3,bool),fun(X3,bool),hAPP(fun(X3,fun(fun(X3,bool),bool)),fun(fun(X3,bool),fun(X3,bool)),combc(X3,fun(X3,bool),bool),member(X3)),X40)))
    <=> hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X41),X40)) ),
    file('<stdin>',fact_208_pred__subset__eq) ).

fof(c_0_59,axiom,
    ! [X2,X3,X1,X37,X38] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X38),top_top(fun(X1,bool)))))
     => hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),combb(X3,X2,X1),X37),X38)),top_top(fun(X1,bool))))) ),
    file('<stdin>',fact_493_finite__range__imageI) ).

fof(c_0_60,axiom,
    ! [X6,X7,X8,X9] :
      ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X6),X7)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X8),X9)))
    <=> ( ti(arrow_490897120le_alt,X6) != ti(arrow_490897120le_alt,X9)
        & ( ti(arrow_490897120le_alt,X7) = ti(arrow_490897120le_alt,X9)
         => ti(arrow_490897120le_alt,X6) != ti(arrow_490897120le_alt,X7) )
        & ( ti(arrow_490897120le_alt,X7) != ti(arrow_490897120le_alt,X9)
         => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X6),X7)),X8)) ) ) ),
    file('<stdin>',fact_5_in__mktop) ).

fof(c_0_61,axiom,
    ! [X6,X7,X8,X9] :
      ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X6),X7)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X8),X9)))
    <=> ( ti(arrow_490897120le_alt,X7) != ti(arrow_490897120le_alt,X9)
        & ( ti(arrow_490897120le_alt,X6) = ti(arrow_490897120le_alt,X9)
         => ti(arrow_490897120le_alt,X6) != ti(arrow_490897120le_alt,X7) )
        & ( ti(arrow_490897120le_alt,X6) != ti(arrow_490897120le_alt,X9)
         => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X6),X7)),X8)) ) ) ),
    file('<stdin>',fact_4_in__mkbot) ).

fof(c_0_62,axiom,
    ! [X3,X1,X6,X37,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X37),X39)))
     => hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X3,X1,hAPP(fun(X1,X3),fun(X3,X1),hAPP(fun(X1,bool),fun(fun(X1,X3),fun(X3,X1)),hilbert_inv_into(X1,X3),X39),X37),X6)),X39)) ),
    file('<stdin>',fact_478_inv__into__into) ).

fof(c_0_63,axiom,
    ! [X54,X57,X37] :
      ( ! [X32,X44] :
          ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X32),X44))
         => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,X37,X32)),hAPP(nat,nat,X37,X44))) )
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,X37,X54)),X57)),hAPP(nat,nat,X37,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),X57)))) ),
    file('<stdin>',fact_262_mono__nat__linear__lb) ).

fof(c_0_64,axiom,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,hAPP(nat,arrow_660593299e_indi,hAPP(fun(arrow_660593299e_indi,nat),fun(nat,arrow_660593299e_indi),hAPP(fun(arrow_660593299e_indi,bool),fun(fun(arrow_660593299e_indi,nat),fun(nat,arrow_660593299e_indi)),hilbert_inv_into(arrow_660593299e_indi,nat),top_top(fun(arrow_660593299e_indi,bool))),h),n)))),
    file('<stdin>',fact_12__096c_A_060_092_060_094bsub_062P_A_Iinv_Ah_An_J_092_060_094esub_062_Ad_0) ).

fof(c_0_65,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X29,X54,X37] :
          ( ! [X44] : hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(nat,X3,X37,X44)),hAPP(nat,X3,X37,hAPP(nat,nat,suc,X44))))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(nat,X3,X37,X29)),hAPP(nat,X3,X37,X54)))
          <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X29),X54)) ) ) ),
    file('<stdin>',fact_443_lift__Suc__mono__less__iff) ).

fof(c_0_66,axiom,
    ! [X3,X1,X37,X39,X43] :
      ( hBOOL(hAPP(fun(fun(X3,X1),bool),bool,hAPP(fun(X3,X1),fun(fun(fun(X3,X1),bool),bool),member(fun(X3,X1)),X37),hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool)),pi(X3,X1),X39),hAPP(fun(X1,bool),fun(X3,fun(X1,bool)),combk(fun(X1,bool),X3),X43))))
     => hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X37),X39)),X43)) ),
    file('<stdin>',fact_463_funcset__image) ).

fof(c_0_67,axiom,
    ! [X3,X1,X39,X43,X37] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),top_top(fun(X3,bool))))
     => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X37),X39)),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X37),X43)))
      <=> hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43)) ) ),
    file('<stdin>',fact_468_inj__image__subset__iff) ).

fof(c_0_68,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X29,X72,X37] :
          ( ! [X44] : hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(nat,X3,X37,X44)),hAPP(nat,X3,X37,hAPP(nat,nat,suc,X44))))
         => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X29),X72))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(nat,X3,X37,X29)),hAPP(nat,X3,X37,X72))) ) ) ),
    file('<stdin>',fact_442_lift__Suc__mono__less) ).

fof(c_0_69,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X29,X72,X37] :
          ( ! [X44] : hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(nat,X3,X37,X44)),hAPP(nat,X3,X37,hAPP(nat,nat,suc,X44))))
         => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X29),X72))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(nat,X3,X37,X29)),hAPP(nat,X3,X37,X72))) ) ) ),
    file('<stdin>',fact_441_lift__Suc__mono__le) ).

fof(c_0_70,axiom,
    ! [X39,X57] :
      ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),X39),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X57),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X57),hAPP(fun(nat,bool),nat,finite_card(nat),X39)))))
     => X39 = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X57),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X57),hAPP(fun(nat,bool),nat,finite_card(nat),X39))) ),
    file('<stdin>',fact_494_subset__card__intvl__is__intvl) ).

fof(c_0_71,axiom,
    ! [X3,X1,X37,X39,X43] :
      ( hBOOL(hAPP(fun(fun(X3,X1),bool),bool,hAPP(fun(X3,X1),fun(fun(fun(X3,X1),bool),bool),member(fun(X3,X1)),X37),hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool)),pi(X3,X1),X39),hAPP(fun(X1,bool),fun(X3,fun(X1,bool)),combk(fun(X1,bool),X3),X43))))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),X39))
       => ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43))
         => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X3,bool),nat,finite_card(X3),X39)),hAPP(fun(X1,bool),nat,finite_card(X1),X43))) ) ) ),
    file('<stdin>',fact_274_card__inj) ).

fof(c_0_72,axiom,
    ! [X1,X3,X39,X37,X6,X7] :
      ( hAPP(X1,X3,hAPP(fun(X3,X1),fun(X1,X3),hAPP(fun(X3,bool),fun(fun(X3,X1),fun(X1,X3)),hilbert_inv_into(X3,X1),X39),X37),X6) = hAPP(X1,X3,hAPP(fun(X3,X1),fun(X1,X3),hAPP(fun(X3,bool),fun(fun(X3,X1),fun(X1,X3)),hilbert_inv_into(X3,X1),X39),X37),X7)
     => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X37),X39)))
       => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X7),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X37),X39)))
         => ti(X1,X6) = ti(X1,X7) ) ) ),
    file('<stdin>',fact_477_inv__into__injective) ).

fof(c_0_73,axiom,
    ! [X3,X1,X6,X37,X39,X43] :
      ( hBOOL(hAPP(fun(fun(X3,X1),bool),bool,hAPP(fun(X3,X1),fun(fun(fun(X3,X1),bool),bool),member(fun(X3,X1)),X37),hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool)),pi(X3,X1),X39),hAPP(fun(X1,bool),fun(X3,fun(X1,bool)),combk(fun(X1,bool),X3),X43))))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X39))
       => hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X3,X1,X37,X6)),X43)) ) ),
    file('<stdin>',fact_140_funcset__mem) ).

fof(c_0_74,axiom,
    ! [X1,X3,X43,X48,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X48),X39))
     => hBOOL(hAPP(fun(fun(X3,X1),bool),bool,hAPP(fun(fun(X3,X1),bool),fun(fun(fun(X3,X1),bool),bool),ord_less_eq(fun(fun(X3,X1),bool)),hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool)),pi(X3,X1),X39),X43)),hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool)),pi(X3,X1),X48),X43))) ),
    file('<stdin>',fact_156_Pi__anti__mono) ).

fof(c_0_75,axiom,
    ! [X3] :
      ( linorder(X3)
     => ! [X14,X15,X17,X79] :
          ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),hAPP(X3,fun(X3,bool),hAPP(X3,fun(X3,fun(X3,bool)),ord_atLeastLessThan(X3),X14),X15)),hAPP(X3,fun(X3,bool),hAPP(X3,fun(X3,fun(X3,bool)),ord_atLeastLessThan(X3),X17),X79)))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X15),X14))
            | ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X17),X14))
              & hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X15),X79)) ) ) ) ),
    file('<stdin>',fact_462_atLeastLessThan__subset__iff) ).

fof(c_0_76,axiom,
    ! [X1,X3,X37,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X37),X39))),hAPP(fun(X3,bool),nat,finite_card(X3),X39))) ),
    file('<stdin>',fact_469_card__image__le) ).

fof(c_0_77,axiom,
    ! [X3,X37,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),hAPP(fun(X3,bool),fun(X3,bool),hAPP(fun(X3,X3),fun(fun(X3,bool),fun(X3,bool)),image(X3,X3),X37),X39)),X39))
       => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X3),fun(fun(X3,bool),bool),inj_on(X3,X3),X37),X39))
         => hAPP(fun(X3,bool),fun(X3,bool),hAPP(fun(X3,X3),fun(fun(X3,bool),fun(X3,bool)),image(X3,X3),X37),X39) = ti(fun(X3,bool),X39) ) ) ),
    file('<stdin>',fact_465_endo__inj__surj) ).

fof(c_0_78,axiom,
    ! [X3,X1,X6,X37,X39,X43] :
      ( hBOOL(hAPP(fun(fun(X3,X1),bool),bool,hAPP(fun(X3,X1),fun(fun(fun(X3,X1),bool),bool),member(fun(X3,X1)),X37),hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool)),pi(X3,X1),X39),X43)))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X39))
       => hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X3,X1,X37,X6)),hAPP(X3,fun(X1,bool),X43,X6))) ) ),
    file('<stdin>',fact_137_Pi__mem) ).

fof(c_0_79,axiom,
    ! [X3,X1,X6,X37,X39,X43] :
      ( hBOOL(hAPP(fun(fun(X3,X1),bool),bool,hAPP(fun(X3,X1),fun(fun(fun(X3,X1),bool),bool),member(fun(X3,X1)),X37),hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool)),pi(X3,X1),X39),X43)))
     => ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X3,X1,X37,X6)),hAPP(X3,fun(X1,bool),X43,X6)))
       => ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X39)) ) ),
    file('<stdin>',fact_86_PiE) ).

fof(c_0_80,axiom,
    ! [X3,X1,X43,X37,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X43),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X37),X39)))
    <=> ? [X81] :
          ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X81),X39))
          & ti(fun(X3,bool),X43) = hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X37),X81) ) ),
    file('<stdin>',fact_485_subset__image__iff) ).

fof(c_0_81,axiom,
    ! [X3,X1,X39,X37,X43] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),X43))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less(fun(X3,bool)),X39),X43))
       => hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X37),X39)),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X37),X43))) ) ),
    file('<stdin>',fact_495_inj__on__strict__subset) ).

fof(c_0_82,axiom,
    ! [X3,X11] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),hAPP(fun(X3,bool),fun(X3,bool),collect(X3),X11)))
     => ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),hAPP(fun(X3,bool),fun(X3,bool),collect(X3),hAPP(fun(X3,bool),fun(X3,bool),hAPP(fun(bool,bool),fun(fun(X3,bool),fun(X3,bool)),combb(bool,bool,X3),fNot),X11))))
      <=> hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),top_top(fun(X3,bool)))) ) ),
    file('<stdin>',fact_297_finite__Collect__not) ).

fof(c_0_83,axiom,
    ! [X3,X1,X9,X37,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X9),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X37),X39)))
    <=> ? [X26] :
          ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X39))
          & ti(X3,X9) = hAPP(X1,X3,X37,X26) ) ),
    file('<stdin>',fact_482_image__iff) ).

fof(c_0_84,axiom,
    ! [X1,X3,X41,X6,X7] :
      ( hBOOL(hAPP(X1,bool,hAPP(X3,fun(X1,bool),hAPP(fun(product_prod(X3,X1),bool),fun(X3,fun(X1,bool)),in_rel(X3,X1),X41),X6),X7))
    <=> hBOOL(hAPP(fun(product_prod(X3,X1),bool),bool,hAPP(product_prod(X3,X1),fun(fun(product_prod(X3,X1),bool),bool),member(product_prod(X3,X1)),hAPP(X1,product_prod(X3,X1),hAPP(X3,fun(X1,product_prod(X3,X1)),product_Pair(X3,X1),X6),X7)),X41)) ),
    file('<stdin>',fact_269_in__rel__def) ).

fof(c_0_85,axiom,
    ! [X3,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39))
     => hBOOL(hAPP(fun(fun(X3,bool),bool),bool,finite_finite_1(fun(X3,bool)),hAPP(fun(fun(X3,bool),bool),fun(fun(X3,bool),bool),collect(fun(X3,bool)),hAPP(fun(X3,bool),fun(fun(X3,bool),bool),hAPP(fun(fun(X3,bool),fun(fun(X3,bool),bool)),fun(fun(X3,bool),fun(fun(X3,bool),bool)),combc(fun(X3,bool),fun(X3,bool),bool),ord_less_eq(fun(X3,bool))),X39)))) ),
    file('<stdin>',fact_279_finite__Collect__subsets) ).

fof(c_0_86,axiom,
    ! [X2,X3,X1,X37] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),top_top(fun(X3,bool))))
     => hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,fun(X2,X1)),fun(fun(X3,bool),bool),inj_on(X3,fun(X2,X1)),hAPP(fun(X3,X1),fun(X3,fun(X2,X1)),hAPP(fun(X1,fun(X2,X1)),fun(fun(X3,X1),fun(X3,fun(X2,X1))),combb(X1,fun(X2,X1),X3),combk(X1,X2)),X37)),top_top(fun(X3,bool)))) ),
    file('<stdin>',fact_89_inj__fun) ).

fof(c_0_87,axiom,
    ! [X6,X8] :
      ( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X8),arrow_2064824852le_Lin))
     => hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X8),X6)),arrow_2064824852le_Lin)) ),
    file('<stdin>',fact_49_mkbot__Lin) ).

fof(c_0_88,axiom,
    ! [X6,X8] :
      ( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X8),arrow_2064824852le_Lin))
     => hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X8),X6)),arrow_2064824852le_Lin)) ),
    file('<stdin>',fact_48_mktop__Lin) ).

fof(c_0_89,axiom,
    ! [X3] :
      ( ordere236663937imp_le(X3)
     => ! [X14,X17,X15] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X14),X17)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X15),X17)))
        <=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X14),X15)) ) ),
    file('<stdin>',fact_181_add__less__cancel__right) ).

fof(c_0_90,axiom,
    ! [X3] :
      ( ordere236663937imp_le(X3)
     => ! [X17,X14,X15] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X17),X14)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X17),X15)))
        <=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X14),X15)) ) ),
    file('<stdin>',fact_180_add__less__cancel__left) ).

fof(c_0_91,axiom,
    ! [X3] :
      ( ordere236663937imp_le(X3)
     => ! [X21,X36,X22] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X36)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X22),X36)))
         => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X22)) ) ),
    file('<stdin>',fact_176_add__less__imp__less__right) ).

fof(c_0_92,axiom,
    ! [X3] :
      ( ordere236663937imp_le(X3)
     => ! [X36,X21,X22] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X36),X21)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X36),X22)))
         => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X22)) ) ),
    file('<stdin>',fact_175_add__less__imp__less__left) ).

fof(c_0_93,axiom,
    ! [X3] :
      ( ordere236663937imp_le(X3)
     => ! [X14,X17,X15] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X14),X17)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X15),X17)))
        <=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X14),X15)) ) ),
    file('<stdin>',fact_174_add__le__cancel__right) ).

fof(c_0_94,axiom,
    ! [X3] :
      ( ordere236663937imp_le(X3)
     => ! [X17,X14,X15] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X17),X14)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X17),X15)))
        <=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X14),X15)) ) ),
    file('<stdin>',fact_173_add__le__cancel__left) ).

fof(c_0_95,axiom,
    ! [X3] :
      ( ordere236663937imp_le(X3)
     => ! [X21,X36,X22] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X36)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X22),X36)))
         => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X21),X22)) ) ),
    file('<stdin>',fact_169_add__le__imp__le__right) ).

fof(c_0_96,axiom,
    ! [X3] :
      ( ordere236663937imp_le(X3)
     => ! [X36,X21,X22] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X36),X21)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X36),X22)))
         => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X21),X22)) ) ),
    file('<stdin>',fact_168_add__le__imp__le__left) ).

fof(c_0_97,axiom,
    ! [X1,X3,X37,X39,X43] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43))
     => hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X37),X39)),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X37),X43))) ),
    file('<stdin>',fact_486_image__mono) ).

fof(c_0_98,axiom,
    ! [X57,X54,X29] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X57),X54)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X57),X29)))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X29)) ),
    file('<stdin>',fact_257_nat__add__left__cancel__le) ).

fof(c_0_99,axiom,
    ! [X57,X54,X29] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X57),X54)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X57),X29)))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X29)) ),
    file('<stdin>',fact_242_nat__add__left__cancel__less) ).

fof(c_0_100,axiom,
    ! [X3,X1] :
      ( ord(X1)
     => ! [X37,X38] :
          ( ! [X26] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X3,X1,X37,X26)),hAPP(X3,X1,X38,X26)))
         => hBOOL(hAPP(fun(X3,X1),bool,hAPP(fun(X3,X1),fun(fun(X3,X1),bool),ord_less_eq(fun(X3,X1)),X37),X38)) ) ),
    file('<stdin>',fact_182_le__funI) ).

fof(c_0_101,axiom,
    ! [X3,X1] :
      ( ord(X1)
     => ! [X37,X38] :
          ( hBOOL(hAPP(fun(X3,X1),bool,hAPP(fun(X3,X1),fun(fun(X3,X1),bool),ord_less_eq(fun(X3,X1)),X37),X38))
        <=> ! [X26] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X3,X1,X37,X26)),hAPP(X3,X1,X38,X26))) ) ),
    file('<stdin>',fact_108_le__fun__def) ).

fof(c_0_102,axiom,
    ! [X8] :
      ( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X8),arrow_2064824852le_Lin))
     => hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),combk(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),arrow_660593299e_indi),X8)),arrow_1111136790e_Prof)) ),
    file('<stdin>',fact_51_const__Lin__Prof) ).

fof(c_0_103,axiom,
    ! [X1,X3,X37,X38,X39] :
      ( ! [X19] :
          ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X19),X39))
         => hAPP(X3,X1,X37,X19) = hAPP(X3,X1,X38,X19) )
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),X39))
      <=> hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X38),X39)) ) ),
    file('<stdin>',fact_276_inj__on__cong) ).

fof(c_0_104,axiom,
    ! [X25,X42] :
      ( hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,X25),X42))
    <=> ! [X26] :
          ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X26),arrow_1111136790e_Prof))
         => hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X25,X26) = hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X26,X42) ) ),
    file('<stdin>',fact_142_dictator__def) ).

fof(c_0_105,axiom,
    ! [X3] :
      ( ordere223160158up_add(X3)
     => ! [X36,X45,X21,X22] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X22))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X36),X45))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X36)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X22),X45))) ) ) ),
    file('<stdin>',fact_177_add__strict__mono) ).

fof(c_0_106,axiom,
    ! [X3] :
      ( ordere779506340up_add(X3)
     => ! [X36,X45,X21,X22] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X21),X22))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X36),X45))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X36)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X22),X45))) ) ) ),
    file('<stdin>',fact_170_add__mono) ).

fof(c_0_107,axiom,
    ! [X3] :
      ( ordere223160158up_add(X3)
     => ! [X36,X45,X21,X22] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X21),X22))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X36),X45))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X36)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X22),X45))) ) ) ),
    file('<stdin>',fact_151_add__le__less__mono) ).

fof(c_0_108,axiom,
    ! [X3] :
      ( ordere223160158up_add(X3)
     => ! [X36,X45,X21,X22] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X22))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X36),X45))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X36)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X22),X45))) ) ) ),
    file('<stdin>',fact_150_add__less__le__mono) ).

fof(c_0_109,axiom,
    ! [X42,X63,X37] :
      ( ! [X16,X64] :
          ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X16),X64))
         => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,X37,X16)),hAPP(nat,nat,X37,X64))) )
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X42),X63))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X37,X42)),hAPP(nat,nat,X37,X63))) ) ),
    file('<stdin>',fact_263_less__mono__imp__le__mono) ).

fof(c_0_110,axiom,
    ! [X52,X61,X58,X59] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X58),X59))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X52),X61))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X58),X52)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X59),X61))) ) ),
    file('<stdin>',fact_261_add__le__mono) ).

fof(c_0_111,axiom,
    ! [X52,X61,X58,X59] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X58),X59))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X52),X61))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X58),X52)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X59),X61))) ) ),
    file('<stdin>',fact_246_add__less__mono) ).

fof(c_0_112,axiom,
    ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab)),
    file('<stdin>',fact_40__096_Ib_M_Aa_J_A_126_058_ALab_096) ).

fof(c_0_113,axiom,
    ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba)),
    file('<stdin>',fact_39__096_Ia_M_Ab_J_A_126_058_ALba_096) ).

fof(c_0_114,axiom,
    ! [X1,X3,X39,X37] :
      ( hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X37),top_top(fun(X1,bool))) = top_top(fun(X3,bool))
     => hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X37),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),hAPP(fun(X1,X3),fun(X3,X1),hAPP(fun(X1,bool),fun(fun(X1,X3),fun(X3,X1)),hilbert_inv_into(X1,X3),top_top(fun(X1,bool))),X37)),X39)) = ti(fun(X3,bool),X39) ),
    file('<stdin>',fact_496_image__surj__f__inv__f) ).

fof(c_0_115,axiom,
    ! [X3,X1,X7,X37,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X7),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X37),X39)))
     => hAPP(X1,X3,X37,hAPP(X3,X1,hAPP(fun(X1,X3),fun(X3,X1),hAPP(fun(X1,bool),fun(fun(X1,X3),fun(X3,X1)),hilbert_inv_into(X1,X3),X39),X37),X7)) = ti(X3,X7) ),
    file('<stdin>',fact_479_f__inv__into__f) ).

fof(c_0_116,axiom,
    ! [X3] :
      ( linordered_idom(X3)
     => ! [X14] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X14),X14)),zero_zero(X3)))
        <=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X14),zero_zero(X3))) ) ),
    file('<stdin>',fact_370_even__less__0__iff) ).

fof(c_0_117,axiom,
    ! [X3] :
      ( linord219039673up_add(X3)
     => ! [X14] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X14),X14)),zero_zero(X3)))
        <=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X14),zero_zero(X3))) ) ),
    file('<stdin>',fact_349_double__add__less__zero__iff__single__add__less__zero) ).

fof(c_0_118,axiom,
    ! [X3] :
      ( linord219039673up_add(X3)
     => ! [X14] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X14),X14)),zero_zero(X3)))
        <=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X14),zero_zero(X3))) ) ),
    file('<stdin>',fact_344_double__add__le__zero__iff__single__add__le__zero) ).

fof(c_0_119,axiom,
    ! [X3] :
      ( ring_1(X3)
     => ! [X15,X14] :
          ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X14),ring_1_Ints(X3)))
         => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X15),ring_1_Ints(X3)))
           => hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X14),X15)),ring_1_Ints(X3))) ) ) ),
    file('<stdin>',fact_476_Ints__add) ).

fof(c_0_120,axiom,
    ! [X3,X39,X43] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X43))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43))
       => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X3,bool),nat,finite_card(X3),X39)),hAPP(fun(X3,bool),nat,finite_card(X3),X43)))
         => hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less(fun(X3,bool)),X39),X43)) ) ) ),
    file('<stdin>',fact_280_card__psubset) ).

fof(c_0_121,axiom,
    ! [X58,X59,X52] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X58),X59)),X52))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X58),X52)) ),
    file('<stdin>',fact_248_add__lessD1) ).

fof(c_0_122,axiom,
    ! [X51,X52,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),X52)),X53))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X52),X53)) ),
    file('<stdin>',fact_220_add__leD2) ).

fof(c_0_123,axiom,
    ! [X51,X52,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),X52)),X53))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X51),X53)) ),
    file('<stdin>',fact_219_add__leD1) ).

fof(c_0_124,axiom,
    ! [X51,X52,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),X52)),X53))
     => ~ ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X51),X53))
         => ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X52),X53)) ) ),
    file('<stdin>',fact_218_add__leE) ).

fof(c_0_125,axiom,
    ! [X3] :
      ( ordere223160158up_add(X3)
     => ! [X36,X21,X22] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X22))
         => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X36)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X22),X36))) ) ),
    file('<stdin>',fact_179_add__strict__right__mono) ).

fof(c_0_126,axiom,
    ! [X3] :
      ( ordere223160158up_add(X3)
     => ! [X36,X21,X22] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X22))
         => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X36),X21)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X36),X22))) ) ),
    file('<stdin>',fact_178_add__strict__left__mono) ).

fof(c_0_127,axiom,
    ! [X3] :
      ( ordere779506340up_add(X3)
     => ! [X36,X21,X22] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X21),X22))
         => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X36)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X22),X36))) ) ),
    file('<stdin>',fact_172_add__right__mono) ).

fof(c_0_128,axiom,
    ! [X3] :
      ( ordere779506340up_add(X3)
     => ! [X36,X21,X22] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X21),X22))
         => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X36),X21)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X36),X22))) ) ),
    file('<stdin>',fact_171_add__left__mono) ).

fof(c_0_129,axiom,
    ! [X52,X58,X59] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X58),X59))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X58),X52)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X59),X52))) ),
    file('<stdin>',fact_260_add__le__mono1) ).

fof(c_0_130,axiom,
    ! [X52,X58,X59] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X58),X59))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X58),X52)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X59),X52))) ),
    file('<stdin>',fact_245_add__less__mono1) ).

fof(c_0_131,axiom,
    ! [X3,X37,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),hAPP(fun(X3,bool),fun(X3,bool),hAPP(fun(X3,X3),fun(fun(X3,bool),fun(X3,bool)),image(X3,X3),X37),X39)))
       => hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X3),fun(fun(X3,bool),bool),inj_on(X3,X3),X37),X39)) ) ),
    file('<stdin>',fact_464_finite__surj__inj) ).

fof(c_0_132,axiom,
    ! [X3] :
      ( ordere216010020id_add(X3)
     => ! [X22,X21] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),zero_zero(X3)))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X22),zero_zero(X3)))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X22)),zero_zero(X3))) ) ) ),
    file('<stdin>',fact_358_add__neg__nonpos) ).

fof(c_0_133,axiom,
    ! [X3] :
      ( ordere216010020id_add(X3)
     => ! [X22,X21] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X21),zero_zero(X3)))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X22),zero_zero(X3)))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X22)),zero_zero(X3))) ) ) ),
    file('<stdin>',fact_357_add__nonpos__neg) ).

fof(c_0_134,axiom,
    ! [X3] :
      ( ordere216010020id_add(X3)
     => ! [X22,X21] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),zero_zero(X3)))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X22),zero_zero(X3)))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X22)),zero_zero(X3))) ) ) ),
    file('<stdin>',fact_346_add__neg__neg) ).

fof(c_0_135,axiom,
    ! [X3] :
      ( ordere216010020id_add(X3)
     => ! [X22,X21] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X21),zero_zero(X3)))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X22),zero_zero(X3)))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X22)),zero_zero(X3))) ) ) ),
    file('<stdin>',fact_339_add__nonpos__nonpos) ).

fof(c_0_136,axiom,
    ! [X3,X39] : hBOOL(hAPP(fun(fun(X3,X3),bool),bool,hAPP(fun(X3,X3),fun(fun(fun(X3,X3),bool),bool),member(fun(X3,X3)),combi(X3)),hAPP(fun(X3,fun(X3,bool)),fun(fun(X3,X3),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X3,bool)),fun(fun(X3,X3),bool)),pi(X3,X3),X39),hAPP(fun(X3,bool),fun(X3,fun(X3,bool)),combk(fun(X3,bool),X3),X39)))),
    file('<stdin>',fact_141_funcset__id) ).

fof(c_0_137,axiom,
    ! [X59,X58] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X59),X58)),X58)),
    file('<stdin>',fact_241_not__add__less2) ).

fof(c_0_138,axiom,
    ! [X58,X59] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X58),X59)),X58)),
    file('<stdin>',fact_240_not__add__less1) ).

fof(c_0_139,axiom,
    ! [X3,X39] :
      ( ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39))
       => hAPP(fun(X3,bool),nat,finite_card(X3),X39) = hAPP(fun(X3,bool),nat,hAPP(nat,fun(fun(X3,bool),nat),hAPP(fun(X3,nat),fun(nat,fun(fun(X3,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(X3,nat),fun(nat,fun(fun(X3,bool),nat))),finite_fold_image(nat,X3),plus_plus(nat)),hAPP(nat,fun(X3,nat),combk(nat,X3),one_one(nat))),zero_zero(nat)),X39) )
      & ( ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39))
       => hAPP(fun(X3,bool),nat,finite_card(X3),X39) = zero_zero(nat) ) ),
    file('<stdin>',fact_455_card__def) ).

fof(c_0_140,axiom,
    ! [X3,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39))
     => hAPP(fun(X3,bool),nat,finite_card(X3),X39) = hAPP(fun(X3,bool),nat,hAPP(nat,fun(fun(X3,bool),nat),hAPP(fun(X3,nat),fun(nat,fun(fun(X3,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(X3,nat),fun(nat,fun(fun(X3,bool),nat))),finite_fold_image(nat,X3),plus_plus(nat)),hAPP(nat,fun(X3,nat),combk(nat,X3),one_one(nat))),zero_zero(nat)),X39) ),
    file('<stdin>',fact_454_card_Oeq__fold__g) ).

fof(c_0_141,axiom,
    ! [X3,X39,X43] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X43))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43))
       => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X3,bool),nat,finite_card(X3),X43)),hAPP(fun(X3,bool),nat,finite_card(X3),X39)))
         => ti(fun(X3,bool),X39) = ti(fun(X3,bool),X43) ) ) ),
    file('<stdin>',fact_300_card__seteq) ).

fof(c_0_142,axiom,
    ! [X57,X60] : hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,nat),fun(fun(nat,bool),bool),inj_on(nat,nat),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),X57)),X60)),
    file('<stdin>',fact_239_inj__on__add__nat) ).

fof(c_0_143,axiom,
    ! [X57] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),X57)))),
    file('<stdin>',fact_285_finite__Collect__le__nat) ).

fof(c_0_144,axiom,
    ! [X57] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X57)))),
    file('<stdin>',fact_284_finite__Collect__less__nat) ).

fof(c_0_145,axiom,
    ! [X3] :
      ( comm_semiring_1(X3)
     => ! [X21,X22,X36,X45] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X22)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X36),X45)) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X36)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X22),X45)) ),
    file('<stdin>',fact_432_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).

fof(c_0_146,axiom,
    ! [X1,X3,X37,X6,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X39))
     => hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X3,X1,X37,X6)),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X37),X39))) ),
    file('<stdin>',fact_481_imageI) ).

fof(c_0_147,axiom,
    ! [X54,X29] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),X29)))
    <=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X54))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X29)) ) ),
    file('<stdin>',fact_355_add__gr__0) ).

fof(c_0_148,axiom,
    ! [X3,X1,X39,X43] :
      ( hBOOL(hAPP(fun(sum_sum(X3,X1),bool),bool,finite_finite_1(sum_sum(X3,X1)),hAPP(fun(X1,bool),fun(sum_sum(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X1,bool),fun(sum_sum(X3,X1),bool)),sum_Plus(X3,X1),X39),X43)))
     => hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43)) ),
    file('<stdin>',fact_309_finite__PlusD_I2_J) ).

fof(c_0_149,axiom,
    ! [X3,X1,X39,X43] :
      ( hBOOL(hAPP(fun(sum_sum(X3,X1),bool),bool,finite_finite_1(sum_sum(X3,X1)),hAPP(fun(X1,bool),fun(sum_sum(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X1,bool),fun(sum_sum(X3,X1),bool)),sum_Plus(X3,X1),X39),X43)))
     => hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39)) ),
    file('<stdin>',fact_308_finite__PlusD_I1_J) ).

fof(c_0_150,axiom,
    ! [X3,X1,X39,X43] :
      ( hBOOL(hAPP(fun(sum_sum(X3,X1),bool),bool,finite_finite_1(sum_sum(X3,X1)),hAPP(fun(X1,bool),fun(sum_sum(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X1,bool),fun(sum_sum(X3,X1),bool)),sum_Plus(X3,X1),X39),X43)))
    <=> ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39))
        & hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43)) ) ),
    file('<stdin>',fact_306_finite__Plus__iff) ).

fof(c_0_151,axiom,
    ! [X1,X3,X50,X11] :
      ( ! [X26,X46] :
          ( hBOOL(hAPP(X1,bool,hAPP(X3,fun(X1,bool),X11,X26),X46))
         => hBOOL(hAPP(X1,bool,hAPP(X3,fun(X1,bool),X50,X26),X46)) )
     => hBOOL(hAPP(fun(X3,fun(X1,bool)),bool,hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,fun(X1,bool)),bool),ord_less_eq(fun(X3,fun(X1,bool))),X11),X50)) ),
    file('<stdin>',fact_209_predicate2I) ).

fof(c_0_152,axiom,
    ! [X3] :
      ( ordere216010020id_add(X3)
     => ! [X22,X21] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),X21))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X22))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X22))) ) ) ),
    file('<stdin>',fact_362_add__pos__nonneg) ).

fof(c_0_153,axiom,
    ! [X3] :
      ( ordere216010020id_add(X3)
     => ! [X22,X21] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X21))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),X22))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X22))) ) ) ),
    file('<stdin>',fact_361_add__nonneg__pos) ).

fof(c_0_154,axiom,
    ! [X3] :
      ( ordere216010020id_add(X3)
     => ! [X22,X21] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),X21))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),X22))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X22))) ) ) ),
    file('<stdin>',fact_348_add__pos__pos) ).

fof(c_0_155,axiom,
    ! [X3] :
      ( ordere216010020id_add(X3)
     => ! [X22,X21] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X21))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X22))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X22))) ) ) ),
    file('<stdin>',fact_343_add__nonneg__nonneg) ).

fof(c_0_156,axiom,
    ! [X1,X3,X2,X37,X38] : hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),hAPP(fun(X1,X2),fun(X1,X3),hAPP(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3)),combb(X2,X3,X1),X37),X38)),top_top(fun(X1,bool))) = hAPP(fun(X2,bool),fun(X3,bool),hAPP(fun(X2,X3),fun(fun(X2,bool),fun(X3,bool)),image(X2,X3),X37),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),top_top(fun(X1,bool)))),
    file('<stdin>',fact_490_range__composition) ).

fof(c_0_157,axiom,
    ! [X14,X15] :
      ( ti(arrow_490897120le_alt,X14) != ti(arrow_490897120le_alt,X15)
     => ? [X26] :
          ( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X26),arrow_2064824852le_Lin))
          & hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X14),X15)),X26)) ) ),
    file('<stdin>',fact_87_complete__Lin) ).

fof(c_0_158,axiom,
    ! [X3] :
      ( ordere216010020id_add(X3)
     => ! [X22,X36,X21] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),X21))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X22),X36))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X22),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X36))) ) ) ),
    file('<stdin>',fact_360_add__strict__increasing) ).

fof(c_0_159,axiom,
    ! [X3] :
      ( ordere216010020id_add(X3)
     => ! [X22,X36,X21] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X21))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X22),X36))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X22),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X36))) ) ) ),
    file('<stdin>',fact_359_add__strict__increasing2) ).

fof(c_0_160,axiom,
    ! [X3] :
      ( linordered_semidom(X3)
     => ! [X22,X36,X21] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),X21))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X22),X36))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X22),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X36))) ) ) ),
    file('<stdin>',fact_347_pos__add__strict) ).

fof(c_0_161,axiom,
    ! [X3] :
      ( ordere216010020id_add(X3)
     => ! [X22,X36,X21] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X21))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X22),X36))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X22),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X36))) ) ) ),
    file('<stdin>',fact_341_add__increasing) ).

fof(c_0_162,axiom,
    ! [X3] :
      ( ordere216010020id_add(X3)
     => ! [X22,X21,X36] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X36))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X22),X21))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X22),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X36))) ) ) ),
    file('<stdin>',fact_340_add__increasing2) ).

fof(c_0_163,axiom,
    ! [X3] :
      ( linordered_field(X3)
     => ! [X33,X34] :
          ( ! [X75] :
              ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),X75))
             => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X33),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X34),X75))) )
         => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X33),X34)) ) ),
    file('<stdin>',fact_453_field__le__epsilon) ).

fof(c_0_164,axiom,
    ~ ! [X31] :
        ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),X31))
       => ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X31),arrow_2064824852le_Lin)) ),
    file('<stdin>',fact_43__096_B_Bthesis_O_A_I_B_BLba_O_A_091_124_Ab_A_060_092_060_094bsub_062Lba_) ).

fof(c_0_165,axiom,
    ~ ! [X30] :
        ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),X30))
       => ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X30),arrow_2064824852le_Lin)) ),
    file('<stdin>',fact_42__096_B_Bthesis_O_A_I_B_BLab_O_A_091_124_Aa_A_060_092_060_094bsub_062Lab_) ).

fof(c_0_166,axiom,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba)),
    file('<stdin>',fact_38__096b_A_060_092_060_094bsub_062Lba_092_060_094esub_062_Aa_096) ).

fof(c_0_167,axiom,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab)),
    file('<stdin>',fact_37__096a_A_060_092_060_094bsub_062Lab_092_060_094esub_062_Ab_096) ).

fof(c_0_168,axiom,
    ! [X1,X3,X2,X37,X38,X39] : hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X37),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),X39)) = hAPP(fun(X2,bool),fun(X3,bool),hAPP(fun(X2,X3),fun(fun(X2,bool),fun(X3,bool)),image(X2,X3),hAPP(fun(X2,X1),fun(X2,X3),hAPP(fun(X1,X3),fun(fun(X2,X1),fun(X2,X3)),combb(X1,X3,X2),X37),X38)),X39),
    file('<stdin>',fact_483_image__image) ).

fof(c_0_169,axiom,
    ! [X3] :
      ( dense_linorder(X3)
     => ! [X35,X33,X34] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X34))
         => ( ! [X47] :
                ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X47))
               => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X47),X34))
                 => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X47),X35)) ) )
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X34),X35)) ) ) ),
    file('<stdin>',fact_154_dense__le__bounded) ).

fof(c_0_170,axiom,
    ! [X3,X1,X6,X7,X37,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),X39))
     => ( hAPP(X3,X1,X37,X6) = hAPP(X3,X1,X37,X7)
       => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X39))
         => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X7),X39))
           => ti(X3,X6) = ti(X3,X7) ) ) ) ),
    file('<stdin>',fact_136_inj__onD) ).

fof(c_0_171,axiom,
    ! [X3,X1,X7,X6,X37,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),X39))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X39))
       => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X7),X39))
         => ( hAPP(X3,X1,X37,X6) = hAPP(X3,X1,X37,X7)
          <=> ti(X3,X6) = ti(X3,X7) ) ) ) ),
    file('<stdin>',fact_135_inj__on__iff) ).

fof(c_0_172,axiom,
    ! [X3,X1,X6,X7,X37,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),X39))
     => ( ti(X3,X6) != ti(X3,X7)
       => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X39))
         => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X7),X39))
           => hAPP(X3,X1,X37,X6) != hAPP(X3,X1,X37,X7) ) ) ) ),
    file('<stdin>',fact_134_inj__on__contraD) ).

fof(c_0_173,axiom,
    ! [X3,X1,X37,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),X39))
    <=> ! [X26] :
          ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X26),X39))
         => ! [X27] :
              ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X27),X39))
             => ( hAPP(X3,X1,X37,X26) = hAPP(X3,X1,X37,X27)
               => ti(X3,X26) = ti(X3,X27) ) ) ) ),
    file('<stdin>',fact_133_inj__on__def) ).

fof(c_0_174,axiom,
    ! [X1,X3,X15,X37,X6,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X39))
     => ( ti(X1,X15) = hAPP(X3,X1,X37,X6)
       => hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X15),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X37),X39))) ) ),
    file('<stdin>',fact_480_rev__image__eqI) ).

fof(c_0_175,axiom,
    ! [X3,X1,X39,X15,X37,X6] :
      ( ti(X3,X15) = hAPP(X1,X3,X37,X6)
     => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X39))
       => hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X15),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X37),X39))) ) ),
    file('<stdin>',fact_458_image__eqI) ).

fof(c_0_176,axiom,
    ! [X3,X1,X11] :
      ( ! [X18] : hBOOL(hAPP(product_prod(X3,X1),bool,X11,X18))
    <=> ! [X19,X20] : hBOOL(hAPP(product_prod(X3,X1),bool,X11,hAPP(X1,product_prod(X3,X1),hAPP(X3,fun(X1,product_prod(X3,X1)),product_Pair(X3,X1),X19),X20))) ),
    file('<stdin>',fact_15_split__paired__All) ).

fof(c_0_177,axiom,
    ! [X3] :
      ( linord219039673up_add(X3)
     => ! [X14] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X14),X14)))
        <=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),X14)) ) ),
    file('<stdin>',fact_350_zero__less__double__add__iff__zero__less__single__add) ).

fof(c_0_178,axiom,
    ! [X3] :
      ( linord219039673up_add(X3)
     => ! [X14] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X14),X14)))
        <=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X14)) ) ),
    file('<stdin>',fact_345_zero__le__double__add__iff__zero__le__single__add) ).

fof(c_0_179,axiom,
    ! [X3,X1,X6,X37,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),X39))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X39))
       => hAPP(X1,X3,hAPP(fun(X3,X1),fun(X1,X3),hAPP(fun(X3,bool),fun(fun(X3,X1),fun(X1,X3)),hilbert_inv_into(X3,X1),X39),X37),hAPP(X3,X1,X37,X6)) = ti(X3,X6) ) ),
    file('<stdin>',fact_145_inv__into__f__f) ).

fof(c_0_180,axiom,
    ! [X3,X1,X6,X7,X11,X50] :
      ( hBOOL(hAPP(fun(X3,fun(X1,bool)),bool,hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,fun(X1,bool)),bool),ord_less_eq(fun(X3,fun(X1,bool))),X11),X50))
     => ( hBOOL(hAPP(X1,bool,hAPP(X3,fun(X1,bool),X11,X6),X7))
       => hBOOL(hAPP(X1,bool,hAPP(X3,fun(X1,bool),X50,X6),X7)) ) ),
    file('<stdin>',fact_197_predicate2D) ).

fof(c_0_181,axiom,
    ! [X1,X3,X50,X11,X6,X7] :
      ( hBOOL(hAPP(X1,bool,hAPP(X3,fun(X1,bool),X11,X6),X7))
     => ( hBOOL(hAPP(fun(X3,fun(X1,bool)),bool,hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,fun(X1,bool)),bool),ord_less_eq(fun(X3,fun(X1,bool))),X11),X50))
       => hBOOL(hAPP(X1,bool,hAPP(X3,fun(X1,bool),X50,X6),X7)) ) ),
    file('<stdin>',fact_195_rev__predicate2D) ).

fof(c_0_182,axiom,
    ! [X3,X39,X43] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X43))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X3,bool),nat,finite_card(X3),X39)),hAPP(fun(X3,bool),nat,finite_card(X3),X43))) ) ),
    file('<stdin>',fact_282_card__mono) ).

fof(c_0_183,axiom,
    ! [X3,X39,X43] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X43))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less(fun(X3,bool)),X39),X43))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X3,bool),nat,finite_card(X3),X39)),hAPP(fun(X3,bool),nat,finite_card(X3),X43))) ) ),
    file('<stdin>',fact_281_psubset__card__mono) ).

fof(c_0_184,axiom,
    ! [X3,X1,X7,X6,X37,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),X39))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X39))
       => ( hAPP(X3,X1,X37,X6) = ti(X1,X7)
         => hAPP(X1,X3,hAPP(fun(X3,X1),fun(X1,X3),hAPP(fun(X3,bool),fun(fun(X3,X1),fun(X1,X3)),hilbert_inv_into(X3,X1),X39),X37),X7) = ti(X3,X6) ) ) ),
    file('<stdin>',fact_146_inv__into__f__eq) ).

fof(c_0_185,axiom,
    ! [X11,X54,X29] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X29))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X11,X29),X54)) )
     => ( ( X54 = X29
         => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X11,X29),X54)) )
       => ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X29),X54))
           => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X11,X29),X54)) )
         => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X11,X29),X54)) ) ) ),
    file('<stdin>',fact_227_nat__less__cases) ).

fof(c_0_186,axiom,
    ! [X58,X51] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X58),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X58),X51)))),
    file('<stdin>',fact_412_less__add__Suc1) ).

fof(c_0_187,axiom,
    ! [X58,X51] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X58),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),X58)))),
    file('<stdin>',fact_411_less__add__Suc2) ).

fof(c_0_188,axiom,
    ! [X3,X49,X39,X43] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less(fun(X3,bool)),X39),X43))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less(fun(X3,bool)),X43),X49))
       => hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less(fun(X3,bool)),X39),X49)) ) ),
    file('<stdin>',fact_215_psubset__trans) ).

fof(c_0_189,axiom,
    ! [X3,X49,X39,X43] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X43),X49))
       => hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X49)) ) ),
    file('<stdin>',fact_198_subset__trans) ).

fof(c_0_190,axiom,
    ! [X3,X49,X39,X43] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less(fun(X3,bool)),X43),X49))
       => hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less(fun(X3,bool)),X39),X49)) ) ),
    file('<stdin>',fact_194_subset__psubset__trans) ).

fof(c_0_191,axiom,
    ! [X3,X49,X39,X43] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less(fun(X3,bool)),X39),X43))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X43),X49))
       => hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less(fun(X3,bool)),X39),X49)) ) ),
    file('<stdin>',fact_193_psubset__subset__trans) ).

fof(c_0_192,axiom,
    ! [X51,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X51)),hAPP(nat,nat,suc,X53)))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),X53)) ),
    file('<stdin>',fact_401_Suc__less__SucD) ).

fof(c_0_193,axiom,
    ! [X54,X29] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X54)),hAPP(nat,nat,suc,X29)))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X29)) ),
    file('<stdin>',fact_393_Suc__less__eq) ).

fof(c_0_194,axiom,
    ! [X29,X54] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X29)),hAPP(nat,nat,suc,X54)))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X29),X54)) ),
    file('<stdin>',fact_380_Suc__le__mono) ).

fof(c_0_195,axiom,
    ! [X3,X1,X37,X6] : hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),hAPP(X1,X3,X37,X6)),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X37),top_top(fun(X1,bool))))),
    file('<stdin>',fact_492_rangeI) ).

fof(c_0_196,axiom,
    ! [X3,X1,X39,X37,X43] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),X43))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43))
       => hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),X39)) ) ),
    file('<stdin>',fact_159_subset__inj__on) ).

fof(c_0_197,axiom,
    ! [X52,X58,X59] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X58),X59))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X59),X52))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X58)),X52)) ) ),
    file('<stdin>',fact_398_less__trans__Suc) ).

fof(c_0_198,axiom,
    ! [X3,X1,X38,X37] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),top_top(fun(X3,bool))))
     => ( ! [X26] : hAPP(X3,X1,X37,hAPP(X1,X3,X38,X26)) = ti(X1,X26)
       => hAPP(fun(X3,X1),fun(X1,X3),hAPP(fun(X3,bool),fun(fun(X3,X1),fun(X1,X3)),hilbert_inv_into(X3,X1),top_top(fun(X3,bool))),X37) = ti(fun(X1,X3),X38) ) ),
    file('<stdin>',fact_148_inj__imp__inv__eq) ).

fof(c_0_199,axiom,
    ! [X3] :
      ( comm_semiring_1(X3)
     => ! [X21,X22,X36] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X22)),X36) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X36)),X22) ),
    file('<stdin>',fact_431_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).

fof(c_0_200,axiom,
    ! [X1,X3,X43,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39))
     => ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43))
       => hBOOL(hAPP(fun(sum_sum(X3,X1),bool),bool,finite_finite_1(sum_sum(X3,X1)),hAPP(fun(X1,bool),fun(sum_sum(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X1,bool),fun(sum_sum(X3,X1),bool)),sum_Plus(X3,X1),X39),X43))) ) ),
    file('<stdin>',fact_307_finite__Plus) ).

fof(c_0_201,axiom,
    ! [X3,X17,X39,X43] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less(fun(X3,bool)),X39),X43))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X17),X39))
       => hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X17),X43)) ) ),
    file('<stdin>',fact_214_psubsetD) ).

fof(c_0_202,axiom,
    ! [X3,X6,X39,X43] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X39))
       => hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X43)) ) ),
    file('<stdin>',fact_202_in__mono) ).

fof(c_0_203,axiom,
    ! [X3,X43,X6,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X39))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43))
       => hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X43)) ) ),
    file('<stdin>',fact_200_set__rev__mp) ).

fof(c_0_204,axiom,
    ! [X3,X6,X39,X43] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X39))
       => hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X43)) ) ),
    file('<stdin>',fact_199_set__mp) ).

fof(c_0_205,axiom,
    ! [X3,X17,X39,X43] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X17),X39))
       => hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X17),X43)) ) ),
    file('<stdin>',fact_189_subsetD) ).

fof(c_0_206,axiom,
    ! [X3,X1] :
      ( ord(X1)
     => ! [X6,X37,X38] :
          ( hBOOL(hAPP(fun(X3,X1),bool,hAPP(fun(X3,X1),fun(fun(X3,X1),bool),ord_less_eq(fun(X3,X1)),X37),X38))
         => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X3,X1,X37,X6)),hAPP(X3,X1,X38,X6))) ) ),
    file('<stdin>',fact_104_le__funD) ).

fof(c_0_207,axiom,
    ! [X3,X1] :
      ( ord(X1)
     => ! [X6,X37,X38] :
          ( hBOOL(hAPP(fun(X3,X1),bool,hAPP(fun(X3,X1),fun(fun(X3,X1),bool),ord_less_eq(fun(X3,X1)),X37),X38))
         => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X3,X1,X37,X6)),hAPP(X3,X1,X38,X6))) ) ),
    file('<stdin>',fact_94_le__funE) ).

fof(c_0_208,axiom,
    ! [X54,X29] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X29))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X29)),X54)) ),
    file('<stdin>',fact_378_not__less__eq__eq) ).

fof(c_0_209,axiom,
    ! [X3] :
      ( linorder(X3)
     => ! [X14,X15,X17,X79] :
          ( hAPP(X3,fun(X3,bool),hAPP(X3,fun(X3,fun(X3,bool)),ord_atLeastLessThan(X3),X14),X15) = hAPP(X3,fun(X3,bool),hAPP(X3,fun(X3,fun(X3,bool)),ord_atLeastLessThan(X3),X17),X79)
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X14),X15))
           => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X17),X79))
             => ti(X3,X15) = ti(X3,X79) ) ) ) ),
    file('<stdin>',fact_489_atLeastLessThan__inj_I2_J) ).

fof(c_0_210,axiom,
    ! [X3] :
      ( linorder(X3)
     => ! [X14,X15,X17,X79] :
          ( hAPP(X3,fun(X3,bool),hAPP(X3,fun(X3,fun(X3,bool)),ord_atLeastLessThan(X3),X14),X15) = hAPP(X3,fun(X3,bool),hAPP(X3,fun(X3,fun(X3,bool)),ord_atLeastLessThan(X3),X17),X79)
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X14),X15))
           => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X17),X79))
             => ti(X3,X14) = ti(X3,X17) ) ) ) ),
    file('<stdin>',fact_488_atLeastLessThan__inj_I1_J) ).

fof(c_0_211,axiom,
    ! [X3] :
      ( linorder(X3)
     => ! [X17,X79,X14,X15] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X14),X15))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X17),X79))
           => ( hAPP(X3,fun(X3,bool),hAPP(X3,fun(X3,fun(X3,bool)),ord_atLeastLessThan(X3),X14),X15) = hAPP(X3,fun(X3,bool),hAPP(X3,fun(X3,fun(X3,bool)),ord_atLeastLessThan(X3),X17),X79)
            <=> ( ti(X3,X14) = ti(X3,X17)
                & ti(X3,X15) = ti(X3,X79) ) ) ) ) ),
    file('<stdin>',fact_487_atLeastLessThan__eq__iff) ).

fof(c_0_212,axiom,
    ! [X3,X1] :
      ( ord(X1)
     => ! [X37,X38] :
          ( hBOOL(hAPP(fun(X3,X1),bool,hAPP(fun(X3,X1),fun(fun(X3,X1),bool),ord_less(fun(X3,X1)),X37),X38))
        <=> ( hBOOL(hAPP(fun(X3,X1),bool,hAPP(fun(X3,X1),fun(fun(X3,X1),bool),ord_less_eq(fun(X3,X1)),X37),X38))
            & ~ hBOOL(hAPP(fun(X3,X1),bool,hAPP(fun(X3,X1),fun(fun(X3,X1),bool),ord_less_eq(fun(X3,X1)),X38),X37)) ) ) ),
    file('<stdin>',fact_155_less__fun__def) ).

fof(c_0_213,axiom,
    ! [X1,X3,X43,X39] :
      ( ( ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39))
          & hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43)) )
       => hAPP(fun(sum_sum(X3,X1),bool),nat,finite_card(sum_sum(X3,X1)),hAPP(fun(X1,bool),fun(sum_sum(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X1,bool),fun(sum_sum(X3,X1),bool)),sum_Plus(X3,X1),X39),X43)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X3,bool),nat,finite_card(X3),X39)),hAPP(fun(X1,bool),nat,finite_card(X1),X43)) )
      & ( ~ ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39))
            & hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43)) )
       => hAPP(fun(sum_sum(X3,X1),bool),nat,finite_card(sum_sum(X3,X1)),hAPP(fun(X1,bool),fun(sum_sum(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X1,bool),fun(sum_sum(X3,X1),bool)),sum_Plus(X3,X1),X39),X43)) = zero_zero(nat) ) ),
    file('<stdin>',fact_317_card__Plus__conv__if) ).

fof(c_0_214,axiom,
    ! [X1,X3,X43,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39))
     => ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43))
       => hAPP(fun(sum_sum(X3,X1),bool),nat,finite_card(sum_sum(X3,X1)),hAPP(fun(X1,bool),fun(sum_sum(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X1,bool),fun(sum_sum(X3,X1),bool)),sum_Plus(X3,X1),X39),X43)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X3,bool),nat,finite_card(X3),X39)),hAPP(fun(X1,bool),nat,finite_card(X1),X43)) ) ),
    file('<stdin>',fact_302_card__Plus) ).

fof(c_0_215,axiom,
    ! [X1,X3,X37,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),X39))
      <=> hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X37),X39)) = hAPP(fun(X3,bool),nat,finite_card(X3),X39) ) ),
    file('<stdin>',fact_471_inj__on__iff__eq__card) ).

fof(c_0_216,axiom,
    ! [X1,X3,X37,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39))
     => ( hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X37),X39)) = hAPP(fun(X3,bool),nat,finite_card(X3),X39)
       => hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),X39)) ) ),
    file('<stdin>',fact_470_eq__card__imp__inj__on) ).

fof(c_0_217,axiom,
    ! [X35,X33,X34] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X33),X34))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X33),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X34),X35))) ),
    file('<stdin>',fact_267_termination__basic__simps_I1_J) ).

fof(c_0_218,axiom,
    ! [X34,X33,X35] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X33),X35))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X33),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X34),X35))) ),
    file('<stdin>',fact_266_termination__basic__simps_I2_J) ).

fof(c_0_219,axiom,
    ! [X34,X33,X35] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X33),X35))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X33),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X34),X35))) ),
    file('<stdin>',fact_265_termination__basic__simps_I4_J) ).

fof(c_0_220,axiom,
    ! [X35,X33,X34] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X33),X34))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X33),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X34),X35))) ),
    file('<stdin>',fact_264_termination__basic__simps_I3_J) ).

fof(c_0_221,axiom,
    ! [X51,X58,X59] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X58),X59))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X58),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),X59))) ),
    file('<stdin>',fact_259_trans__le__add2) ).

fof(c_0_222,axiom,
    ! [X51,X58,X59] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X58),X59))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X58),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X59),X51))) ),
    file('<stdin>',fact_258_trans__le__add1) ).

fof(c_0_223,axiom,
    ! [X51,X58,X59] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X58),X59))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X58),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),X59))) ),
    file('<stdin>',fact_244_trans__less__add2) ).

fof(c_0_224,axiom,
    ! [X51,X58,X59] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X58),X59))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X58),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X59),X51))) ),
    file('<stdin>',fact_243_trans__less__add1) ).

fof(c_0_225,axiom,
    ! [X58,X52] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X58)),X52))
     => ~ ! [X64] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X58),X64))
           => X52 != hAPP(nat,nat,suc,X64) ) ),
    file('<stdin>',fact_448_Suc__lessE) ).

fof(c_0_226,axiom,
    ! [X29,X54] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X29),X54))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X29)),X54)) ),
    file('<stdin>',fact_409_less__eq__Suc__le) ).

fof(c_0_227,axiom,
    ! [X54,X29] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X54)),X29))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X29)) ),
    file('<stdin>',fact_407_Suc__le__eq) ).

fof(c_0_228,axiom,
    ! [X51,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X51)),X53))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),X53)) ),
    file('<stdin>',fact_403_Suc__le__lessD) ).

fof(c_0_229,axiom,
    ! [X51,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X51)),X53))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),X53)) ),
    file('<stdin>',fact_400_Suc__lessD) ).

fof(c_0_230,axiom,
    ! [X51,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X51)),X53))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X51),X53)) ),
    file('<stdin>',fact_383_Suc__leD) ).

fof(c_0_231,axiom,
    ! [X3,X1,X15,X37,X6] :
      ( ti(X3,X15) = hAPP(X1,X3,X37,X6)
     => hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X15),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X37),top_top(fun(X1,bool))))) ),
    file('<stdin>',fact_491_range__eqI) ).

fof(c_0_232,axiom,
    ! [X51,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),X53))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X51)),hAPP(nat,nat,suc,X53))) ),
    file('<stdin>',fact_375_Suc__mono) ).

fof(c_0_233,axiom,
    ! [X3,X39,X43] :
      ( ti(fun(X3,bool),X39) = ti(fun(X3,bool),X43)
    <=> ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43))
        & hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X43),X39)) ) ),
    file('<stdin>',fact_206_set__eq__subset) ).

fof(c_0_234,axiom,
    ! [X3,X39,X43] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X43),X39))
       => ti(fun(X3,bool),X39) = ti(fun(X3,bool),X43) ) ),
    file('<stdin>',fact_188_equalityI) ).

fof(c_0_235,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X35,X34,X33] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X34),X33))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X35),X34))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X35),X33)) ) ) ),
    file('<stdin>',fact_129_xt1_I8_J) ).

fof(c_0_236,axiom,
    ! [X3] :
      ( preorder(X3)
     => ! [X35,X33,X34] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X33),X34))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X34),X35))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X35)) ) ) ),
    file('<stdin>',fact_128_order__le__less__trans) ).

fof(c_0_237,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X35,X34,X33] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X34),X33))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X35),X34))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X35),X33)) ) ) ),
    file('<stdin>',fact_127_xt1_I7_J) ).

fof(c_0_238,axiom,
    ! [X3] :
      ( preorder(X3)
     => ! [X35,X33,X34] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X34))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X34),X35))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X35)) ) ) ),
    file('<stdin>',fact_126_order__less__le__trans) ).

fof(c_0_239,axiom,
    ! [X3] :
      ( preorder(X3)
     => ! [X35,X33,X34] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X33),X34))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X34),X35))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X33),X35)) ) ) ),
    file('<stdin>',fact_97_order__trans) ).

fof(c_0_240,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X35,X34,X33] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X34),X33))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X35),X34))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X35),X33)) ) ) ),
    file('<stdin>',fact_95_xt1_I6_J) ).

fof(c_0_241,axiom,
    ! [X3] :
      ( preorder(X3)
     => ! [X35,X33,X34] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X34))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X34),X35))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X35)) ) ) ),
    file('<stdin>',fact_55_order__less__trans) ).

fof(c_0_242,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X35,X34,X33] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X34),X33))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X35),X34))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X35),X33)) ) ) ),
    file('<stdin>',fact_54_xt1_I10_J) ).

fof(c_0_243,axiom,
    ! [X3,X1,X6,X37] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),top_top(fun(X3,bool))))
     => hAPP(X1,X3,hAPP(fun(X3,X1),fun(X1,X3),hAPP(fun(X3,bool),fun(fun(X3,X1),fun(X1,X3)),hilbert_inv_into(X3,X1),top_top(fun(X3,bool))),X37),hAPP(X3,X1,X37,X6)) = ti(X3,X6) ),
    file('<stdin>',fact_84_inv__f__f) ).

fof(c_0_244,axiom,
    hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),p),arrow_1111136790e_Prof)),
    file('<stdin>',fact_3__096P_A_058_AProf_096) ).

fof(c_0_245,axiom,
    ! [X3,X1,X6,X7,X37] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),top_top(fun(X3,bool))))
     => ( hAPP(X3,X1,X37,X6) = ti(X1,X7)
       => hAPP(X1,X3,hAPP(fun(X3,X1),fun(X1,X3),hAPP(fun(X3,bool),fun(fun(X3,X1),fun(X1,X3)),hilbert_inv_into(X3,X1),top_top(fun(X3,bool))),X37),X7) = ti(X3,X6) ) ),
    file('<stdin>',fact_83_inv__f__eq) ).

fof(c_0_246,axiom,
    ! [X52,X58,X59] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X58),X59))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X59),X52))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X58),X52)) ) ),
    file('<stdin>',fact_236_le__trans) ).

fof(c_0_247,axiom,
    arrow_1111136790e_Prof = hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(arrow_660593299e_indi,bool),fun(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),top_top(fun(arrow_660593299e_indi,bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),arrow_660593299e_indi),arrow_2064824852le_Lin)),
    file('<stdin>',fact_138_Prof__def) ).

fof(c_0_248,axiom,
    ! [X51,X53,X52,X61] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X52),X61))
     => ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),X61) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X52),X53)
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),X53)) ) ),
    file('<stdin>',fact_247_less__add__eq__less) ).

fof(c_0_249,axiom,
    ! [X3] :
      ( comm_semiring_1(X3)
     => ! [X21,X22,X36] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X22)),X36) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X22),X36)) ),
    file('<stdin>',fact_430_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).

fof(c_0_250,axiom,
    ! [X3] :
      ( comm_semiring_1(X3)
     => ! [X21,X36,X45] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X36),X45)) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X36)),X45) ),
    file('<stdin>',fact_429_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).

fof(c_0_251,axiom,
    ! [X3] :
      ( ab_semigroup_add(X3)
     => ! [X21,X22,X36] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X22)),X36) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X22),X36)) ),
    file('<stdin>',fact_166_ab__semigroup__add__class_Oadd__ac_I1_J) ).

fof(c_0_252,axiom,
    ! [X54,X29] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X29))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X29),hAPP(nat,nat,suc,X54)))
      <=> X29 = X54 ) ),
    file('<stdin>',fact_404_le__less__Suc__eq) ).

fof(c_0_253,axiom,
    ! [X54,X29] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X29))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X29),hAPP(nat,nat,suc,X54))) ),
    file('<stdin>',fact_391_not__less__eq) ).

fof(c_0_254,axiom,
    ! [X3] :
      ( ordere216010020id_add(X3)
     => ! [X7,X6] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X6))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X7))
           => ( hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X6),X7) = zero_zero(X3)
            <=> ( ti(X3,X6) = zero_zero(X3)
                & ti(X3,X7) = zero_zero(X3) ) ) ) ) ),
    file('<stdin>',fact_342_add__nonneg__eq__0__iff) ).

fof(c_0_255,axiom,
    ! [X51,X53,X52] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),X53)),X52) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X53),X52)),
    file('<stdin>',fact_230_nat__add__assoc) ).

fof(c_0_256,axiom,
    ! [X51,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),X53))
     => ( hAPP(nat,nat,suc,X51) != X53
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X51)),X53)) ) ),
    file('<stdin>',fact_397_Suc__lessI) ).

fof(c_0_257,axiom,
    ! [X51,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),X53))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X51)),X53)) ),
    file('<stdin>',fact_405_Suc__leI) ).

fof(c_0_258,axiom,
    ! [X29] : hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),X29))) = hAPP(nat,nat,suc,X29),
    file('<stdin>',fact_426_card__Collect__le__nat) ).

fof(c_0_259,axiom,
    ! [X1,X3,X76,X25] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X25))
     => hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X76),X25))) ),
    file('<stdin>',fact_459_finite__imageI) ).

fof(c_0_260,axiom,
    ! [X1,X3,X37,X39] :
      ( ! [X26,X46] :
          ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X26),X39))
         => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X46),X39))
           => ( hAPP(X3,X1,X37,X26) = hAPP(X3,X1,X37,X46)
             => ti(X3,X26) = ti(X3,X46) ) ) )
     => hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),X39)) ),
    file('<stdin>',fact_275_inj__onI) ).

fof(c_0_261,axiom,
    ! [X51,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X51),hAPP(nat,nat,suc,X53)))
     => ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X51),X53))
       => X51 = hAPP(nat,nat,suc,X53) ) ),
    file('<stdin>',fact_382_le__SucE) ).

fof(c_0_262,axiom,
    ! [X54,X29] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),hAPP(nat,nat,suc,X29)))
    <=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X29))
        | X54 = hAPP(nat,nat,suc,X29) ) ),
    file('<stdin>',fact_379_le__Suc__eq) ).

fof(c_0_263,axiom,
    ! [X53,X73] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X53)),X73))
     => ? [X32] : X73 = hAPP(nat,nat,suc,X32) ),
    file('<stdin>',fact_446_Suc__le__D) ).

fof(c_0_264,axiom,
    ! [X11,X42,X63] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X42),X63))
     => ( hBOOL(hAPP(nat,bool,X11,X63))
       => ( ! [X16] :
              ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X16),X63))
             => ( hBOOL(hAPP(nat,bool,X11,hAPP(nat,nat,suc,X16)))
               => hBOOL(hAPP(nat,bool,X11,X16)) ) )
         => hBOOL(hAPP(nat,bool,X11,X42)) ) ) ),
    file('<stdin>',fact_438_inc__induct) ).

fof(c_0_265,axiom,
    ! [X3] :
      ( preorder(X3)
     => ! [X6,X7] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X6),X7))
        <=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X6),X7))
            & ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X7),X6)) ) ) ),
    file('<stdin>',fact_113_less__le__not__le) ).

fof(c_0_266,axiom,
    ! [X29] : hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X29))) = X29,
    file('<stdin>',fact_290_card__Collect__less__nat) ).

fof(c_0_267,axiom,
    ! [X54,X29] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),hAPP(nat,nat,suc,X29)))
    <=> ( X54 = zero_zero(nat)
        | ? [X64] :
            ( X54 = hAPP(nat,nat,suc,X64)
            & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X64),X29)) ) ) ),
    file('<stdin>',fact_417_less__Suc__eq__0__disj) ).

fof(c_0_268,axiom,
    ! [X3,X43,X39] :
      ( ! [X26] :
          ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X26),X39))
         => hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X26),X43)) )
     => hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43)) ),
    file('<stdin>',fact_211_subsetI) ).

fof(c_0_269,axiom,
    ! [X3,X37] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),top_top(fun(X3,bool))))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X3),fun(fun(X3,bool),bool),inj_on(X3,X3),X37),top_top(fun(X3,bool))))
       => hAPP(fun(X3,bool),fun(X3,bool),hAPP(fun(X3,X3),fun(fun(X3,bool),fun(X3,bool)),image(X3,X3),X37),top_top(fun(X3,bool))) = top_top(fun(X3,bool)) ) ),
    file('<stdin>',fact_466_finite__UNIV__inj__surj) ).

fof(c_0_270,axiom,
    ! [X51,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),hAPP(nat,nat,suc,X53)))
     => ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),X53))
       => X51 = X53 ) ),
    file('<stdin>',fact_399_less__SucE) ).

fof(c_0_271,axiom,
    ! [X53,X51] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X53),X51))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X53),hAPP(nat,nat,suc,X51)))
       => X51 = X53 ) ),
    file('<stdin>',fact_395_less__antisym) ).

fof(c_0_272,axiom,
    ! [X29,X54] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X29),X54))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X29),hAPP(nat,nat,suc,X54)))
      <=> X29 = X54 ) ),
    file('<stdin>',fact_394_not__less__less__Suc__eq) ).

fof(c_0_273,axiom,
    ! [X54,X29] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),hAPP(nat,nat,suc,X29)))
    <=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X29))
        | X54 = X29 ) ),
    file('<stdin>',fact_392_less__Suc__eq) ).

fof(c_0_274,axiom,
    ! [X54,X29] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),hAPP(nat,nat,suc,X29)))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X29)) ),
    file('<stdin>',fact_408_less__Suc__eq__le) ).

fof(c_0_275,axiom,
    ! [X53] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X53)),X53)),
    file('<stdin>',fact_377_Suc__n__not__le__n) ).

fof(c_0_276,axiom,
    ! [X3,X39,X43] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43))
    <=> ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less(fun(X3,bool)),X39),X43))
        | ti(fun(X3,bool),X39) = ti(fun(X3,bool),X43) ) ),
    file('<stdin>',fact_191_subset__iff__psubset__eq) ).

fof(c_0_277,axiom,
    ! [X3,X39,X43] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less(fun(X3,bool)),X39),X43))
    <=> ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43))
        & ti(fun(X3,bool),X39) != ti(fun(X3,bool),X43) ) ),
    file('<stdin>',fact_190_psubset__eq) ).

fof(c_0_278,axiom,
    ! [X3,X39,X43] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less(fun(X3,bool)),X39),X43))
     => hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43)) ),
    file('<stdin>',fact_192_psubset__imp__subset) ).

fof(c_0_279,axiom,
    ! [X60] :
      ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X60))
    <=> ? [X32] :
        ! [X26] :
          ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X26),X60))
         => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X26),X32)) ) ),
    file('<stdin>',fact_314_finite__nat__set__iff__bounded) ).

fof(c_0_280,axiom,
    ! [X60] :
      ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X60))
    <=> ? [X32] :
        ! [X26] :
          ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X26),X60))
         => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X26),X32)) ) ),
    file('<stdin>',fact_313_finite__nat__set__iff__bounded__le) ).

fof(c_0_281,axiom,
    ! [X29,X11] :
      ( ~ hBOOL(hAPP(nat,bool,X11,zero_zero(nat)))
     => ( hBOOL(hAPP(nat,bool,X11,X29))
       => ? [X62] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X62),X29))
            & ! [X16] :
                ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X16),X62))
               => ~ hBOOL(hAPP(nat,bool,X11,X16)) )
            & hBOOL(hAPP(nat,bool,X11,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X62),one_one(nat)))) ) ) ),
    file('<stdin>',fact_366_ex__least__nat__less) ).

fof(c_0_282,axiom,
    ! [X3] :
      ( linorder(X3)
     => ! [X6,X7] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X6),X7))
         => ( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X6),X7))
          <=> ti(X3,X6) = ti(X3,X7) ) ) ),
    file('<stdin>',fact_122_linorder__antisym__conv2) ).

fof(c_0_283,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X6,X7] :
          ( ti(X3,X6) = ti(X3,X7)
        <=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X6),X7))
            & hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X7),X6)) ) ) ),
    file('<stdin>',fact_106_order__eq__iff) ).

fof(c_0_284,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X7,X6] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X7),X6))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X6),X7))
          <=> ti(X3,X6) = ti(X3,X7) ) ) ),
    file('<stdin>',fact_103_order__antisym__conv) ).

fof(c_0_285,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X33,X34] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X33),X34))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X34),X33))
           => ti(X3,X33) = ti(X3,X34) ) ) ),
    file('<stdin>',fact_98_order__antisym) ).

fof(c_0_286,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X34,X33] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X34),X33))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X33),X34))
           => ti(X3,X33) = ti(X3,X34) ) ) ),
    file('<stdin>',fact_96_xt1_I5_J) ).

fof(c_0_287,axiom,
    ! [X3,X37] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),top_top(fun(X3,bool))))
     => ( hAPP(fun(X3,bool),fun(X3,bool),hAPP(fun(X3,X3),fun(fun(X3,bool),fun(X3,bool)),image(X3,X3),X37),top_top(fun(X3,bool))) = top_top(fun(X3,bool))
       => hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X3),fun(fun(X3,bool),bool),inj_on(X3,X3),X37),top_top(fun(X3,bool)))) ) ),
    file('<stdin>',fact_467_finite__UNIV__surj__inj) ).

fof(c_0_288,axiom,
    ! [X3] :
      ( preorder(X3)
     => ! [X11,X6,X7] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X6),X7))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X7),X6))
           => hBOOL(X11) ) ) ),
    file('<stdin>',fact_62_order__less__imp__triv) ).

fof(c_0_289,axiom,
    ! [X3] :
      ( linorder(X3)
     => ! [X34,X33] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X34),X33))
         => ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X34)) ) ),
    file('<stdin>',fact_120_leD) ).

fof(c_0_290,axiom,
    ! [X3] :
      ( linorder(X3)
     => ! [X6,X7] :
          ( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X6),X7))
        <=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X7),X6)) ) ),
    file('<stdin>',fact_110_linorder__not__le) ).

fof(c_0_291,axiom,
    ! [X3] :
      ( linorder(X3)
     => ! [X6,X7] :
          ( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X6),X7))
        <=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X7),X6)) ) ),
    file('<stdin>',fact_109_linorder__not__less) ).

fof(c_0_292,axiom,
    ! [X3] :
      ( linorder(X3)
     => ! [X6,X7] :
          ( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X6),X7))
        <=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X7),X6))
            | ti(X3,X6) = ti(X3,X7) ) ) ),
    file('<stdin>',fact_71_not__less__iff__gr__or__eq) ).

fof(c_0_293,axiom,
    ! [X3] :
      ( preorder(X3)
     => ! [X33,X34] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X34))
         => ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X34),X33)) ) ),
    file('<stdin>',fact_66_order__less__not__sym) ).

fof(c_0_294,axiom,
    ! [X3] :
      ( preorder(X3)
     => ! [X33,X34] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X34))
         => ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X34),X33)) ) ),
    file('<stdin>',fact_65_order__less__imp__not__less) ).

fof(c_0_295,axiom,
    ! [X3] :
      ( preorder(X3)
     => ! [X21,X22] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X22))
         => ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X22),X21)) ) ),
    file('<stdin>',fact_61_order__less__asym_H) ).

fof(c_0_296,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X22,X21] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X22),X21))
         => ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X22)) ) ),
    file('<stdin>',fact_60_xt1_I9_J) ).

fof(c_0_297,axiom,
    ! [X3] :
      ( preorder(X3)
     => ! [X33,X34] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X34))
         => ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X34),X33)) ) ),
    file('<stdin>',fact_53_order__less__asym) ).

fof(c_0_298,axiom,
    ! [X51,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X51),X53))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),hAPP(nat,nat,suc,X53))) ),
    file('<stdin>',fact_406_le__imp__less__Suc) ).

fof(c_0_299,axiom,
    ! [X51,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),X53))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),hAPP(nat,nat,suc,X53))) ),
    file('<stdin>',fact_396_less__SucI) ).

fof(c_0_300,axiom,
    ! [X51,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X51),X53))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X51),hAPP(nat,nat,suc,X53))) ),
    file('<stdin>',fact_381_le__SucI) ).

fof(c_0_301,axiom,
    ! [X3] :
      ( linordered_semidom(X3)
     => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),one_one(X3)),one_one(X3)))) ),
    file('<stdin>',fact_363_zero__less__two) ).

fof(c_0_302,axiom,
    ! [X51,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X51),X53))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X53),X51))
       => X51 = X53 ) ),
    file('<stdin>',fact_237_le__antisym) ).

fof(c_0_303,axiom,
    ! [X3] :
      ( linordered_semidom(X3)
     => ! [X21] : hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),one_one(X3)))) ),
    file('<stdin>',fact_149_less__add__one) ).

fof(c_0_304,axiom,
    ! [X3] :
      ( comm_semiring_1(X3)
     => ! [X21,X36,X45] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X36),X45)) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X36),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X45)) ),
    file('<stdin>',fact_428_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).

fof(c_0_305,axiom,
    ! [X3] :
      ( dense_linorder(X3)
     => ! [X35,X34] :
          ( ! [X26] :
              ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X26),X34))
             => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X26),X35)) )
         => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X34),X35)) ) ),
    file('<stdin>',fact_153_dense__le) ).

fof(c_0_306,axiom,
    ! [X3,X39] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X3,bool),nat,finite_card(X3),X39)))
     => hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39)) ),
    file('<stdin>',fact_364_card__ge__0__finite) ).

fof(c_0_307,axiom,
    ! [X3,X39,X43] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X43))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43))
       => hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39)) ) ),
    file('<stdin>',fact_292_rev__finite__subset) ).

fof(c_0_308,axiom,
    ! [X3,X39,X43] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43))
     => ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X43))
       => hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39)) ) ),
    file('<stdin>',fact_291_finite__subset) ).

fof(c_0_309,axiom,
    ! [X53,X51] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X53),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X53),X51))),
    file('<stdin>',fact_255_le__add1) ).

fof(c_0_310,axiom,
    ! [X53,X51] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X53),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),X53))),
    file('<stdin>',fact_254_le__add2) ).

fof(c_0_311,axiom,
    ! [X33,X34,X35] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X33),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X34),X35)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X34),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X33),X35)),
    file('<stdin>',fact_229_nat__add__left__commute) ).

fof(c_0_312,axiom,
    ! [X29,X11] :
      ( ~ hBOOL(hAPP(nat,bool,X11,zero_zero(nat)))
     => ( hBOOL(hAPP(nat,bool,X11,X29))
       => ? [X62] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X62),X29))
            & ! [X16] :
                ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X16),X62))
               => ~ hBOOL(hAPP(nat,bool,X11,X16)) )
            & hBOOL(hAPP(nat,bool,X11,X62)) ) ) ),
    file('<stdin>',fact_368_ex__least__nat__le) ).

fof(c_0_313,axiom,
    ! [X3,X50,X11,X6] :
      ( hBOOL(hAPP(X3,bool,X11,X6))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X11),X50))
       => hBOOL(hAPP(X3,bool,X50,X6)) ) ),
    file('<stdin>',fact_205_rev__predicate1D) ).

fof(c_0_314,axiom,
    ! [X3,X6,X11,X50] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X11),X50))
     => ( hBOOL(hAPP(X3,bool,X11,X6))
       => hBOOL(hAPP(X3,bool,X50,X6)) ) ),
    file('<stdin>',fact_201_predicate1D) ).

fof(c_0_315,axiom,
    ! [X3,X39] :
      ( ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),top_top(fun(X3,bool))))
     => ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39))
       => ? [X19] : ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X19),X39)) ) ),
    file('<stdin>',fact_301_ex__new__if__finite) ).

fof(c_0_316,axiom,
    ! [X54,X29] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X29))
    <=> ? [X62] : X29 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),X62)) ),
    file('<stdin>',fact_410_less__iff__Suc__add) ).

fof(c_0_317,axiom,
    ! [X3,X2,X1,X86,X87,X88] : hAPP(X3,X2,hAPP(fun(X3,X1),fun(X3,X2),hAPP(fun(X3,fun(X1,X2)),fun(fun(X3,X1),fun(X3,X2)),combs(X3,X1,X2),X86),X87),X88) = hAPP(X1,X2,hAPP(X3,fun(X1,X2),X86,X88),hAPP(X3,X1,X87,X88)),
    file('<stdin>',help_COMBS_1_1_U) ).

fof(c_0_318,axiom,
    ! [X58,X52] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X58),X52))
     => ( X52 != hAPP(nat,nat,suc,X58)
       => ~ ! [X64] :
              ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X58),X64))
             => X52 != hAPP(nat,nat,suc,X64) ) ) ),
    file('<stdin>',fact_447_lessE) ).

fof(c_0_319,axiom,
    ! [X51,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),X53))
     => ? [X62] : X53 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),X62)) ),
    file('<stdin>',fact_439_less__imp__Suc__add) ).

fof(c_0_320,axiom,
    ! [X3] :
      ( ring_char_0(X3)
     => ! [X14] :
          ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X14),ring_1_Ints(X3)))
         => ( hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X14),X14) = zero_zero(X3)
          <=> ti(X3,X14) = zero_zero(X3) ) ) ),
    file('<stdin>',fact_473_Ints__double__eq__0__iff) ).

fof(c_0_321,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X36,X21,X22] :
          ( ti(X3,X21) = ti(X3,X22)
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X36),X22))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X36),X21)) ) ) ),
    file('<stdin>',fact_101_xt1_I3_J) ).

fof(c_0_322,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X36,X22,X21] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X22),X21))
         => ( ti(X3,X22) = ti(X3,X36)
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X36),X21)) ) ) ),
    file('<stdin>',fact_99_xt1_I4_J) ).

fof(c_0_323,axiom,
    ! [X3] :
      ( linorder(X3)
     => ! [X7,X6] :
          ( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X7),X6))
         => ( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X6),X7))
          <=> ti(X3,X6) = ti(X3,X7) ) ) ),
    file('<stdin>',fact_69_linorder__antisym__conv3) ).

fof(c_0_324,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X36,X21,X22] :
          ( ti(X3,X21) = ti(X3,X22)
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X36),X22))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X36),X21)) ) ) ),
    file('<stdin>',fact_58_xt1_I1_J) ).

fof(c_0_325,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X36,X22,X21] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X22),X21))
         => ( ti(X3,X22) = ti(X3,X36)
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X36),X21)) ) ) ),
    file('<stdin>',fact_56_xt1_I2_J) ).

fof(c_0_326,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X22,X21] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X22),X21))
         => ( ti(X3,X21) != ti(X3,X22)
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X22),X21)) ) ) ),
    file('<stdin>',fact_125_xt1_I11_J) ).

fof(c_0_327,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X21,X22] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X21),X22))
         => ( ti(X3,X21) != ti(X3,X22)
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X22)) ) ) ),
    file('<stdin>',fact_124_order__le__neq__trans) ).

fof(c_0_328,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X33,X34] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X33),X34))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X34))
            | ti(X3,X33) = ti(X3,X34) ) ) ),
    file('<stdin>',fact_123_order__le__imp__less__or__eq) ).

fof(c_0_329,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X21,X22] :
          ( ti(X3,X21) != ti(X3,X22)
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X22),X21))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X22),X21)) ) ) ),
    file('<stdin>',fact_119_xt1_I12_J) ).

fof(c_0_330,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X21,X22] :
          ( ti(X3,X21) != ti(X3,X22)
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X21),X22))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X22)) ) ) ),
    file('<stdin>',fact_118_order__neq__le__trans) ).

fof(c_0_331,axiom,
    ! [X3] :
      ( linorder(X3)
     => ! [X6,X7] :
          ( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X6),X7))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X6),X7))
          <=> ti(X3,X6) = ti(X3,X7) ) ) ),
    file('<stdin>',fact_117_linorder__antisym__conv1) ).

fof(c_0_332,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X6,X7] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X6),X7))
        <=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X6),X7))
            | ti(X3,X6) = ti(X3,X7) ) ) ),
    file('<stdin>',fact_114_order__le__less) ).

fof(c_0_333,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X6,X7] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X6),X7))
        <=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X6),X7))
            & ti(X3,X6) != ti(X3,X7) ) ) ),
    file('<stdin>',fact_112_order__less__le) ).

fof(c_0_334,axiom,
    ! [X3,X1,X6,X7,X37] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),top_top(fun(X3,bool))))
     => ( hAPP(X3,X1,X37,X6) = hAPP(X3,X1,X37,X7)
       => ti(X3,X6) = ti(X3,X7) ) ),
    file('<stdin>',fact_144_injD) ).

fof(c_0_335,axiom,
    ! [X3,X1,X6,X7,X37] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),top_top(fun(X3,bool))))
     => ( hAPP(X3,X1,X37,X6) = hAPP(X3,X1,X37,X7)
      <=> ti(X3,X6) = ti(X3,X7) ) ),
    file('<stdin>',fact_143_inj__eq) ).

fof(c_0_336,axiom,
    ! [X3] :
      ( ord(X3)
     => ! [X36,X21,X22] :
          ( X21 = X22
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X22),X36))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X21),X36)) ) ) ),
    file('<stdin>',fact_102_ord__eq__le__trans) ).

fof(c_0_337,axiom,
    ! [X3] :
      ( ord(X3)
     => ! [X36,X21,X22] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X21),X22))
         => ( X22 = X36
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X21),X36)) ) ) ),
    file('<stdin>',fact_100_ord__le__eq__trans) ).

fof(c_0_338,axiom,
    ! [X3] :
      ( ord(X3)
     => ! [X36,X21,X22] :
          ( X21 = X22
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X22),X36))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X36)) ) ) ),
    file('<stdin>',fact_59_ord__eq__less__trans) ).

fof(c_0_339,axiom,
    ! [X3] :
      ( ord(X3)
     => ! [X36,X21,X22] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X22))
         => ( X22 = X36
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X36)) ) ) ),
    file('<stdin>',fact_57_ord__less__eq__trans) ).

fof(c_0_340,axiom,
    ! [X3] :
      ( preorder(X3)
     => ! [X33,X34] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X34))
         => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X33),X34)) ) ),
    file('<stdin>',fact_121_order__less__imp__le) ).

fof(c_0_341,axiom,
    ! [X77,X66] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X77),X66))),
    file('<stdin>',fact_460_finite__atLeastLessThan) ).

fof(c_0_342,axiom,
    ! [X58,X59] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X58),X59))
     => ? [X62] :
          ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X62))
          & hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X58),X62) = X59 ) ),
    file('<stdin>',fact_369_less__imp__add__positive) ).

fof(c_0_343,axiom,
    ! [X1,X2,X3,X28,X14,X15] : hAPP(product_prod(X1,X2),X3,hAPP(fun(X1,fun(X2,X3)),fun(product_prod(X1,X2),X3),product_prod_rec(X1,X2,X3),X28),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X14),X15)) = hAPP(X2,X3,hAPP(X1,fun(X2,X3),X28,X14),X15),
    file('<stdin>',fact_28_prod_Orecs) ).

fof(c_0_344,axiom,
    ! [X51,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X51),X53))
     => ( X51 != X53
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),X53)) ) ),
    file('<stdin>',fact_252_le__neq__implies__less) ).

fof(c_0_345,axiom,
    ! [X54,X29] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X29))
    <=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X29))
        | X54 = X29 ) ),
    file('<stdin>',fact_250_le__eq__less__or__eq) ).

fof(c_0_346,axiom,
    ! [X54,X29] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X29))
    <=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X29))
        & X54 != X29 ) ),
    file('<stdin>',fact_249_nat__less__le) ).

fof(c_0_347,axiom,
    ! [X33,X34] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X33),X34))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X33),X34)) ),
    file('<stdin>',fact_268_termination__basic__simps_I5_J) ).

fof(c_0_348,axiom,
    ! [X51,X53] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),X53))
        | X51 = X53 )
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X51),X53)) ),
    file('<stdin>',fact_253_less__or__eq__imp__le) ).

fof(c_0_349,axiom,
    ! [X51,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),X53))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X51),X53)) ),
    file('<stdin>',fact_251_less__imp__le__nat) ).

fof(c_0_350,axiom,
    ! [X29] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X29),hAPP(nat,nat,suc,zero_zero(nat))))
    <=> X29 = zero_zero(nat) ),
    file('<stdin>',fact_416_less__Suc0) ).

fof(c_0_351,axiom,
    ! [X3] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),top_top(fun(X3,bool))))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X3,bool),nat,finite_card(X3),top_top(fun(X3,bool))))) ),
    file('<stdin>',fact_365_finite__UNIV__card__ge__0) ).

fof(c_0_352,axiom,
    ? [X65] : hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X65),arrow_2064824852le_Lin)),
    file('<stdin>',fact_271_linear__alt) ).

fof(c_0_353,axiom,
    hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),lba),arrow_2064824852le_Lin)),
    file('<stdin>',fact_35__096Lba_A_058_ALin_096) ).

fof(c_0_354,axiom,
    hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),lab),arrow_2064824852le_Lin)),
    file('<stdin>',fact_34__096Lab_A_058_ALin_096) ).

fof(c_0_355,axiom,
    ! [X29,X11] :
      ( hBOOL(hAPP(nat,bool,X11,zero_zero(nat)))
     => ( ! [X44] :
            ( hBOOL(hAPP(nat,bool,X11,X44))
           => hBOOL(hAPP(nat,bool,X11,hAPP(nat,nat,suc,X44))) )
       => hBOOL(hAPP(nat,bool,X11,X29)) ) ),
    file('<stdin>',fact_452_nat__induct) ).

fof(c_0_356,axiom,
    ! [X3,X2,X1,X86,X87,X88] : hAPP(X3,X2,hAPP(X1,fun(X3,X2),hAPP(fun(X3,fun(X1,X2)),fun(X1,fun(X3,X2)),combc(X3,X1,X2),X86),X87),X88) = hAPP(X1,X2,hAPP(X3,fun(X1,X2),X86,X88),X87),
    file('<stdin>',help_COMBC_1_1_U) ).

fof(c_0_357,axiom,
    ! [X3,X2,X1,X86,X87,X88] : hAPP(X3,X2,hAPP(fun(X3,X1),fun(X3,X2),hAPP(fun(X1,X2),fun(fun(X3,X1),fun(X3,X2)),combb(X1,X2,X3),X86),X87),X88) = hAPP(X1,X2,X86,hAPP(X3,X1,X87,X88)),
    file('<stdin>',help_COMBB_1_1_U) ).

fof(c_0_358,axiom,
    ! [X51,X53] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,X51)),X53) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),X53)),
    file('<stdin>',fact_389_add__Suc) ).

fof(c_0_359,axiom,
    ! [X3,X6,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X39))
    <=> hBOOL(hAPP(X3,bool,X39,X6)) ),
    file('<stdin>',fact_76_mem__def) ).

fof(c_0_360,axiom,
    ! [X54,X29] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X29))
    <=> ? [X62] : X29 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),X62) ),
    file('<stdin>',fact_256_le__iff__add) ).

fof(c_0_361,axiom,
    ! [X3] :
      ( linordered_idom(X3)
     => ! [X33,X34] :
          ( ti(X3,X33) != ti(X3,X34)
         => ( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X34))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X34),X33)) ) ) ),
    file('<stdin>',fact_160_linorder__neqE__linordered__idom) ).

fof(c_0_362,axiom,
    ! [X3] :
      ( linorder(X3)
     => ! [X6,X7] :
          ( ti(X3,X6) != ti(X3,X7)
        <=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X6),X7))
            | hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X7),X6)) ) ) ),
    file('<stdin>',fact_72_linorder__neq__iff) ).

fof(c_0_363,axiom,
    ! [X3] :
      ( linorder(X3)
     => ! [X33,X34] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X34))
          | ti(X3,X33) = ti(X3,X34)
          | hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X34),X33)) ) ),
    file('<stdin>',fact_70_linorder__less__linear) ).

fof(c_0_364,axiom,
    ! [X3] :
      ( linorder(X3)
     => ! [X33,X34] :
          ( ti(X3,X33) != ti(X3,X34)
         => ( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X34))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X34),X33)) ) ) ),
    file('<stdin>',fact_68_linorder__neqE) ).

fof(c_0_365,axiom,
    ! [X3] :
      ( linorder(X3)
     => ! [X33,X34] :
          ( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X34))
         => ( ti(X3,X33) != ti(X3,X34)
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X34),X33)) ) ) ),
    file('<stdin>',fact_52_linorder__cases) ).

fof(c_0_366,axiom,
    ! [X3] :
      ( linorder(X3)
     => ! [X34,X33] :
          ( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X34),X33))
         => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X34)) ) ),
    file('<stdin>',fact_116_not__leE) ).

fof(c_0_367,axiom,
    ! [X3] :
      ( linorder(X3)
     => ! [X33,X34] :
          ( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X34))
         => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X34),X33)) ) ),
    file('<stdin>',fact_115_leI) ).

fof(c_0_368,axiom,
    ! [X3] :
      ( linorder(X3)
     => ! [X33,X34] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X33),X34))
          | hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X34),X33)) ) ),
    file('<stdin>',fact_111_linorder__le__less__linear) ).

fof(c_0_369,axiom,
    ! [X3] :
      ( linorder(X3)
     => ! [X33,X34] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X33),X34))
          | hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X34),X33)) ) ),
    file('<stdin>',fact_107_linorder__linear) ).

fof(c_0_370,axiom,
    ! [X3] :
      ( linorder(X3)
     => ! [X33,X34] :
          ( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X33),X34))
         => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X34),X33)) ) ),
    file('<stdin>',fact_93_linorder__le__cases) ).

fof(c_0_371,axiom,
    ! [X29,X60] :
      ( ! [X26] :
          ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X26),X60))
         => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X26),X29)) )
     => hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X60)) ),
    file('<stdin>',fact_316_bounded__nat__set__is__finite) ).

fof(c_0_372,axiom,
    ! [X3,X1] :
      ( hBOOL(hAPP(fun(sum_sum(X3,X1),bool),bool,finite_finite_1(sum_sum(X3,X1)),top_top(fun(sum_sum(X3,X1),bool))))
    <=> ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),top_top(fun(X3,bool))))
        & hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool)))) ) ),
    file('<stdin>',fact_295_finite__Plus__UNIV__iff) ).

fof(c_0_373,axiom,
    ! [X1,X3] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),top_top(fun(X3,bool))))
     => ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool))))
       => hBOOL(hAPP(fun(product_prod(X3,X1),bool),bool,finite_finite_1(product_prod(X3,X1)),top_top(fun(product_prod(X3,X1),bool)))) ) ),
    file('<stdin>',fact_294_finite__Prod__UNIV) ).

fof(c_0_374,axiom,
    ! [X33,X34] :
      ( X33 != X34
     => ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X33),X34))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X34),X33)) ) ),
    file('<stdin>',fact_223_linorder__neqE__nat) ).

fof(c_0_375,axiom,
    ! [X54,X29] :
      ( X54 != X29
    <=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X29))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X29),X54)) ) ),
    file('<stdin>',fact_222_nat__neq__iff) ).

fof(c_0_376,axiom,
    ! [X51,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X51),X53))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X53),X51)) ),
    file('<stdin>',fact_234_nat__le__linear) ).

fof(c_0_377,axiom,
    ! [X1,X3,X14,X15,X12,X13] :
      ( hAPP(X1,product_prod(X3,X1),hAPP(X3,fun(X1,product_prod(X3,X1)),product_Pair(X3,X1),X14),X15) = hAPP(X1,product_prod(X3,X1),hAPP(X3,fun(X1,product_prod(X3,X1)),product_Pair(X3,X1),X12),X13)
    <=> ( ti(X3,X14) = ti(X3,X12)
        & ti(X1,X15) = ti(X1,X13) ) ),
    file('<stdin>',fact_22_Pair__eq) ).

fof(c_0_378,axiom,
    ! [X1,X3,X21,X22,X23,X24] :
      ( hAPP(X1,product_prod(X3,X1),hAPP(X3,fun(X1,product_prod(X3,X1)),product_Pair(X3,X1),X21),X22) = hAPP(X1,product_prod(X3,X1),hAPP(X3,fun(X1,product_prod(X3,X1)),product_Pair(X3,X1),X23),X24)
     => ~ ( ti(X3,X21) = ti(X3,X23)
         => ti(X1,X22) != ti(X1,X24) ) ),
    file('<stdin>',fact_21_Pair__inject) ).

fof(c_0_379,axiom,
    ! [X3,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39))
     => ( ( ? [X26] : hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X26),X39))
         => one_one(nat) = zero_zero(nat) )
       => hAPP(fun(X3,bool),nat,finite_card(X3),X39) = zero_zero(nat) ) ),
    file('<stdin>',fact_367_card_Oneutral) ).

fof(c_0_380,axiom,
    ! [X51,X53] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),hAPP(nat,nat,suc,X53)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),X53)),
    file('<stdin>',fact_390_add__Suc__right) ).

fof(c_0_381,axiom,
    ! [X51,X53] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,X51)),X53) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),hAPP(nat,nat,suc,X53)),
    file('<stdin>',fact_388_add__Suc__shift) ).

fof(c_0_382,axiom,
    ! [X3,X1] :
      ( hBOOL(hAPP(fun(fun(X3,X1),bool),bool,finite_finite_1(fun(X3,X1)),top_top(fun(fun(X3,X1),bool))))
     => ( hAPP(fun(X1,bool),nat,finite_card(X1),top_top(fun(X1,bool))) != hAPP(nat,nat,suc,zero_zero(nat))
       => hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),top_top(fun(X3,bool)))) ) ),
    file('<stdin>',fact_372_finite__fun__UNIVD1) ).

fof(c_0_383,axiom,
    ! [X3,X1,X37] :
      ( ! [X26,X46] :
          ( hAPP(X3,X1,X37,X26) = hAPP(X3,X1,X37,X46)
         => ti(X3,X26) = ti(X3,X46) )
     => hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),top_top(fun(X3,bool)))) ),
    file('<stdin>',fact_152_injI) ).

fof(c_0_384,axiom,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),n),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool))))),
    file('<stdin>',fact_19_n_I1_J) ).

fof(c_0_385,axiom,
    ! [X11,X57] :
      ( hBOOL(hAPP(nat,bool,X11,X57))
     => ( ! [X44] :
            ( hBOOL(hAPP(nat,bool,X11,hAPP(nat,nat,suc,X44)))
           => hBOOL(hAPP(nat,bool,X11,X44)) )
       => hBOOL(hAPP(nat,bool,X11,zero_zero(nat))) ) ),
    file('<stdin>',fact_451_zero__induct) ).

fof(c_0_386,axiom,
    ! [X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X53))
     => ? [X32] : X53 = hAPP(nat,nat,suc,X32) ),
    file('<stdin>',fact_440_gr0__implies__Suc) ).

fof(c_0_387,axiom,
    ! [X29] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X29))
    <=> ? [X32] : X29 = hAPP(nat,nat,suc,X32) ),
    file('<stdin>',fact_415_gr0__conv__Suc) ).

fof(c_0_388,axiom,
    ~ ! [X78] :
        ( hBOOL(hAPP(fun(arrow_660593299e_indi,bool),bool,hAPP(fun(arrow_660593299e_indi,nat),fun(fun(arrow_660593299e_indi,bool),bool),inj_on(arrow_660593299e_indi,nat),X78),top_top(fun(arrow_660593299e_indi,bool))))
       => hAPP(fun(arrow_660593299e_indi,bool),fun(nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(fun(arrow_660593299e_indi,bool),fun(nat,bool)),image(arrow_660593299e_indi,nat),X78),top_top(fun(arrow_660593299e_indi,bool))) != hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool)))) ),
    file('<stdin>',fact_461__096_B_Bthesis_O_A_I_B_Bh_O_A_091_124_Ainj_Ah_059_Arange_Ah_A_061_A_123) ).

fof(c_0_389,axiom,
    hAPP(fun(arrow_660593299e_indi,bool),fun(nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(fun(arrow_660593299e_indi,bool),fun(nat,bool)),image(arrow_660593299e_indi,nat),h),top_top(fun(arrow_660593299e_indi,bool))) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool)))),
    file('<stdin>',fact_456_surjh) ).

fof(c_0_390,axiom,
    ! [X3,X1,X39] : hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool)),pi(X3,X1),X39),hAPP(fun(X1,bool),fun(X3,fun(X1,bool)),combk(fun(X1,bool),X3),top_top(fun(X1,bool)))) = top_top(fun(fun(X3,X1),bool)),
    file('<stdin>',fact_88_Pi__UNIV) ).

fof(c_0_391,axiom,
    ! [X3] :
      ( linordered_semidom(X3)
     => ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),one_one(X3)),zero_zero(X3))) ),
    file('<stdin>',fact_354_not__one__less__zero) ).

fof(c_0_392,axiom,
    ! [X3] :
      ( linordered_semidom(X3)
     => ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),one_one(X3)),zero_zero(X3))) ),
    file('<stdin>',fact_352_not__one__le__zero) ).

fof(c_0_393,axiom,
    ! [X3] :
      ( top(X3)
     => ! [X21] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),top_top(X3)),X21))
         => ti(X3,X21) = top_top(X3) ) ),
    file('<stdin>',fact_132_top__le) ).

fof(c_0_394,axiom,
    ! [X3] :
      ( top(X3)
     => ! [X14] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),top_top(X3)),X14))
        <=> ti(X3,X14) = top_top(X3) ) ),
    file('<stdin>',fact_131_top__unique) ).

fof(c_0_395,axiom,
    ! [X3] :
      ( cancel_semigroup_add(X3)
     => ! [X14,X15,X17] :
          ( hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X14),X15) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X14),X17)
        <=> ti(X3,X15) = ti(X3,X17) ) ),
    file('<stdin>',fact_165_add__left__cancel) ).

fof(c_0_396,axiom,
    ! [X3] :
      ( cancel_semigroup_add(X3)
     => ! [X15,X14,X17] :
          ( hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X15),X14) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X17),X14)
        <=> ti(X3,X15) = ti(X3,X17) ) ),
    file('<stdin>',fact_164_add__right__cancel) ).

fof(c_0_397,axiom,
    ! [X3] :
      ( cancel_semigroup_add(X3)
     => ! [X21,X22,X36] :
          ( hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X22) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X36)
         => ti(X3,X22) = ti(X3,X36) ) ),
    file('<stdin>',fact_163_add__left__imp__eq) ).

fof(c_0_398,axiom,
    ! [X3] :
      ( cancel146912293up_add(X3)
     => ! [X21,X22,X36] :
          ( hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X22) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X36)
         => ti(X3,X22) = ti(X3,X36) ) ),
    file('<stdin>',fact_162_add__imp__eq) ).

fof(c_0_399,axiom,
    ! [X3] :
      ( cancel_semigroup_add(X3)
     => ! [X22,X21,X36] :
          ( hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X22),X21) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X36),X21)
         => ti(X3,X22) = ti(X3,X36) ) ),
    file('<stdin>',fact_161_add__right__imp__eq) ).

fof(c_0_400,axiom,
    ! [X3] :
      ( top(X3)
     => ! [X14] :
          ( ti(X3,X14) != top_top(X3)
        <=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X14),top_top(X3))) ) ),
    file('<stdin>',fact_31_less__top) ).

fof(c_0_401,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X33,X34] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X34))
         => ti(X3,X33) != ti(X3,X34) ) ),
    file('<stdin>',fact_67_less__imp__neq) ).

fof(c_0_402,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X33,X34] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X34))
         => ti(X3,X33) != ti(X3,X34) ) ),
    file('<stdin>',fact_64_order__less__imp__not__eq) ).

fof(c_0_403,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X33,X34] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X34))
         => ti(X3,X34) != ti(X3,X33) ) ),
    file('<stdin>',fact_63_order__less__imp__not__eq2) ).

fof(c_0_404,axiom,
    ! [X3] :
      ( top(X3)
     => ! [X21] : ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),top_top(X3)),X21)) ),
    file('<stdin>',fact_30_not__top__less) ).

fof(c_0_405,axiom,
    ! [X53] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,X53))),
    file('<stdin>',fact_376_zero__less__Suc) ).

fof(c_0_406,axiom,
    ! [X3,X33,X34] :
      ( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),fequal(X3),X33),X34))
      | ti(X3,X33) = ti(X3,X34) ),
    file('<stdin>',help_fequal_1_1_T) ).

fof(c_0_407,axiom,
    ! [X53] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X53),hAPP(nat,nat,suc,X53))),
    file('<stdin>',fact_374_lessI) ).

fof(c_0_408,axiom,
    ! [X3] :
      ( preorder(X3)
     => ! [X33] : ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X33)) ),
    file('<stdin>',fact_73_order__less__irrefl) ).

fof(c_0_409,axiom,
    ! [X29] :
      ( X29 != zero_zero(nat)
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X29)) ),
    file('<stdin>',fact_323_neq0__conv) ).

fof(c_0_410,axiom,
    ! [X29] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X29),zero_zero(nat)))
    <=> X29 = zero_zero(nat) ),
    file('<stdin>',fact_329_le__0__eq) ).

fof(c_0_411,axiom,
    ! [X53] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X53),zero_zero(nat))),
    file('<stdin>',fact_324_not__less0) ).

fof(c_0_412,axiom,
    ! [X53] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X53),zero_zero(nat))),
    file('<stdin>',fact_322_less__nat__zero__code) ).

fof(c_0_413,axiom,
    ! [X53] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X53),zero_zero(nat))),
    file('<stdin>',fact_318_less__zeroE) ).

fof(c_0_414,axiom,
    ! [X51,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),X53))
     => X53 != zero_zero(nat) ),
    file('<stdin>',fact_321_gr__implies__not0) ).

fof(c_0_415,axiom,
    ! [X55,X56] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X55),X56))
     => X55 != X56 ),
    file('<stdin>',fact_226_less__not__refl3) ).

fof(c_0_416,axiom,
    ! [X53,X51] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X53),X51))
     => X51 != X53 ),
    file('<stdin>',fact_225_less__not__refl2) ).

fof(c_0_417,axiom,
    ! [X53] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X53),X53)),
    file('<stdin>',fact_224_less__irrefl__nat) ).

fof(c_0_418,axiom,
    ! [X53] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X53),X53)),
    file('<stdin>',fact_221_less__not__refl) ).

fof(c_0_419,axiom,
    ! [X54,X57,X29] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),X57) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X29),X57)
    <=> X54 = X29 ),
    file('<stdin>',fact_232_nat__add__right__cancel) ).

fof(c_0_420,axiom,
    ! [X57,X54,X29] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X57),X54) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X57),X29)
    <=> X54 = X29 ),
    file('<stdin>',fact_231_nat__add__left__cancel) ).

fof(c_0_421,axiom,
    ! [X86,X87] :
      ( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X86),X87))
      | hBOOL(X86)
      | hBOOL(X87) ),
    file('<stdin>',help_fdisj_3_1_U) ).

fof(c_0_422,axiom,
    ! [X86,X87] :
      ( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X86),X87))
      | hBOOL(X87) ),
    file('<stdin>',help_fconj_3_1_U) ).

fof(c_0_423,axiom,
    ! [X86,X87] :
      ( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X86),X87))
      | hBOOL(X86) ),
    file('<stdin>',help_fconj_2_1_U) ).

fof(c_0_424,axiom,
    ! [X3,X1,X37,X38] :
      ( ! [X26] : hAPP(X3,X1,X37,X26) = hAPP(X3,X1,X38,X26)
     => ti(fun(X3,X1),X37) = ti(fun(X3,X1),X38) ),
    file('<stdin>',fact_75_ext) ).

fof(c_0_425,axiom,
    ! [X3,X1] :
      ( hBOOL(hAPP(fun(fun(X3,X1),bool),bool,finite_finite_1(fun(X3,X1)),top_top(fun(fun(X3,X1),bool))))
     => hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool)))) ),
    file('<stdin>',fact_299_finite__fun__UNIVD2) ).

fof(c_0_426,axiom,
    ! [X3,X39,X43] :
      ( ti(fun(X3,bool),X39) = ti(fun(X3,bool),X43)
     => hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43)) ),
    file('<stdin>',fact_204_equalityD1) ).

fof(c_0_427,axiom,
    ! [X3,X39,X43] :
      ( ti(fun(X3,bool),X39) = ti(fun(X3,bool),X43)
     => hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X43),X39)) ),
    file('<stdin>',fact_203_equalityD2) ).

fof(c_0_428,axiom,
    ! [X3,X39,X43] :
      ( ti(fun(X3,bool),X39) = ti(fun(X3,bool),X43)
     => ~ ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43))
         => ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X43),X39)) ) ),
    file('<stdin>',fact_196_equalityE) ).

fof(c_0_429,axiom,
    ! [X3,X39] : hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),top_top(fun(X3,bool)))),
    file('<stdin>',fact_158_subset__UNIV) ).

fof(c_0_430,axiom,
    ! [X3,X33,X34] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),hAPP(bool,fun(X3,fun(X3,X3)),if(X3),fFalse),X33),X34) = ti(X3,X34),
    file('<stdin>',help_If_2_1_T) ).

fof(c_0_431,axiom,
    ! [X3,X33,X34] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),hAPP(bool,fun(X3,fun(X3,X3)),if(X3),fTrue),X33),X34) = ti(X3,X33),
    file('<stdin>',help_If_1_1_T) ).

fof(c_0_432,axiom,
    ! [X54,X29] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),X29) = hAPP(nat,nat,suc,zero_zero(nat))
    <=> ( ( X54 = hAPP(nat,nat,suc,zero_zero(nat))
          & X29 = zero_zero(nat) )
        | ( X54 = zero_zero(nat)
          & X29 = hAPP(nat,nat,suc,zero_zero(nat)) ) ) ),
    file('<stdin>',fact_414_add__is__1) ).

fof(c_0_433,axiom,
    ! [X54,X29] :
      ( hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),X29)
    <=> ( ( X54 = hAPP(nat,nat,suc,zero_zero(nat))
          & X29 = zero_zero(nat) )
        | ( X54 = zero_zero(nat)
          & X29 = hAPP(nat,nat,suc,zero_zero(nat)) ) ) ),
    file('<stdin>',fact_413_one__is__add) ).

fof(c_0_434,axiom,
    ! [X3,X39] : hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X39)),
    file('<stdin>',fact_207_subset__refl) ).

fof(c_0_435,axiom,
    ! [X3,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),top_top(fun(X3,bool))))
     => ( hAPP(fun(X3,bool),nat,finite_card(X3),X39) = hAPP(fun(X3,bool),nat,finite_card(X3),top_top(fun(X3,bool)))
       => ti(fun(X3,bool),X39) = top_top(fun(X3,bool)) ) ),
    file('<stdin>',fact_298_card__eq__UNIV__imp__eq__UNIV) ).

fof(c_0_436,axiom,
    ! [X3,X39] : hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X3),fun(fun(X3,bool),bool),inj_on(X3,X3),combi(X3)),X39)),
    file('<stdin>',fact_139_inj__on__id2) ).

fof(c_0_437,axiom,
    hBOOL(hAPP(fun(arrow_660593299e_indi,bool),bool,hAPP(fun(arrow_660593299e_indi,nat),fun(fun(arrow_660593299e_indi,bool),bool),inj_on(arrow_660593299e_indi,nat),h),top_top(fun(arrow_660593299e_indi,bool)))),
    file('<stdin>',fact_20_injh) ).

fof(c_0_438,axiom,
    ! [X3,X1] : ti(fun(fun(X3,fun(X3,X3)),fun(X3,fun(fun(X1,X3),fun(fun(fun(X1,bool),X3),bool)))),finite908156982e_idem(X3,X1)) = finite908156982e_idem(X3,X1),
    file('<stdin>',tsy_c_Finite__Set_Ofolding__image__simple__idem_res) ).

fof(c_0_439,axiom,
    ! [X3,X6] : hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),top_top(fun(X3,bool)))),
    file('<stdin>',fact_27_iso__tuple__UNIV__I) ).

fof(c_0_440,axiom,
    ! [X3,X6] : hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),top_top(fun(X3,bool)))),
    file('<stdin>',fact_26_UNIV__I) ).

fof(c_0_441,axiom,
    ! [X60] : hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,nat),fun(fun(nat,bool),bool),inj_on(nat,nat),suc),X60)),
    file('<stdin>',fact_418_inj__Suc) ).

fof(c_0_442,axiom,
    ! [X3] :
      ( ring_1(X3)
     => hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),one_one(X3)),ring_1_Ints(X3))) ),
    file('<stdin>',fact_475_Ints__1) ).

fof(c_0_443,axiom,
    ! [X3] :
      ( ring_1(X3)
     => hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),zero_zero(X3)),ring_1_Ints(X3))) ),
    file('<stdin>',fact_474_Ints__0) ).

fof(c_0_444,axiom,
    ! [X3] :
      ( hBOOL(hAPP(fun(option(X3),bool),bool,finite_finite_1(option(X3)),top_top(fun(option(X3),bool))))
    <=> hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),top_top(fun(X3,bool)))) ),
    file('<stdin>',fact_296_finite__option__UNIV) ).

fof(c_0_445,axiom,
    ! [X3,X33,X34] :
      ( ti(X3,X33) != ti(X3,X34)
      | hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),fequal(X3),X33),X34)) ),
    file('<stdin>',help_fequal_2_1_T) ).

fof(c_0_446,axiom,
    ! [X3] :
      ( linordered_semidom(X3)
     => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),one_one(X3))) ),
    file('<stdin>',fact_353_zero__less__one) ).

fof(c_0_447,axiom,
    ! [X3] :
      ( linordered_semidom(X3)
     => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),one_one(X3))) ),
    file('<stdin>',fact_351_zero__le__one) ).

fof(c_0_448,axiom,
    ! [X3] :
      ( comm_semiring_1(X3)
     => ! [X21,X36] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X36) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X36),X21) ),
    file('<stdin>',fact_427_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).

fof(c_0_449,axiom,
    ! [X3] :
      ( top(X3)
     => ! [X21] : hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X21),top_top(X3))) ),
    file('<stdin>',fact_130_top__greatest) ).

fof(c_0_450,axiom,
    ! [X1,X3] : hAPP(fun(X1,bool),fun(sum_sum(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X1,bool),fun(sum_sum(X3,X1),bool)),sum_Plus(X3,X1),top_top(fun(X3,bool))),top_top(fun(X1,bool))) = top_top(fun(sum_sum(X3,X1),bool)),
    file('<stdin>',fact_311_UNIV__Plus__UNIV) ).

fof(c_0_451,axiom,
    ! [X3] :
      ( preorder(X3)
     => ! [X33,X34] :
          ( X33 = X34
         => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X33),X34)) ) ),
    file('<stdin>',fact_105_order__eq__refl) ).

fof(c_0_452,axiom,
    ! [X3] :
      ( preorder(X3)
     => ! [X33] : hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X33),X33)) ),
    file('<stdin>',fact_90_order__refl) ).

fof(c_0_453,axiom,
    ! [X53] :
      ( X53 != zero_zero(nat)
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X53)) ),
    file('<stdin>',fact_320_gr0I) ).

fof(c_0_454,axiom,
    ! [X53] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),X53)),
    file('<stdin>',fact_330_less__eq__nat_Osimps_I1_J) ).

fof(c_0_455,axiom,
    ! [X53] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),X53)),
    file('<stdin>',fact_319_le0) ).

fof(c_0_456,axiom,
    ! [X51,X53] :
      ( X51 = X53
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X51),X53)) ),
    file('<stdin>',fact_235_eq__imp__le) ).

fof(c_0_457,axiom,
    ! [X53] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X53),X53)),
    file('<stdin>',fact_233_le__refl) ).

fof(c_0_458,axiom,
    ! [X51,X53] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),X53) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X53),X51),
    file('<stdin>',fact_228_nat__add__commute) ).

fof(c_0_459,axiom,
    ! [X87,X86] :
      ( ~ hBOOL(X86)
      | ~ hBOOL(X87)
      | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X86),X87)) ),
    file('<stdin>',help_fconj_1_1_U) ).

fof(c_0_460,axiom,
    ! [X86,X87] :
      ( ~ hBOOL(X87)
      | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X86),X87)) ),
    file('<stdin>',help_fdisj_2_1_U) ).

fof(c_0_461,axiom,
    ! [X87,X86] :
      ( ~ hBOOL(X86)
      | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X86),X87)) ),
    file('<stdin>',help_fdisj_1_1_U) ).

fof(c_0_462,axiom,
    hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,f)),
    file('<stdin>',fact_1_u) ).

fof(c_0_463,axiom,
    hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,f)),
    file('<stdin>',fact_0_assms_I3_J) ).

fof(c_0_464,axiom,
    ! [X3] :
      ( semiri456707255roduct(X3)
     => ! [X15,X14] :
          ( ti(X3,X15) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X15),X14)
        <=> ti(X3,X14) = zero_zero(X3) ) ),
    file('<stdin>',fact_373_add__0__iff) ).

fof(c_0_465,axiom,
    ! [X3] :
      ( linord219039673up_add(X3)
     => ! [X14] :
          ( hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X14),X14) = zero_zero(X3)
        <=> ti(X3,X14) = zero_zero(X3) ) ),
    file('<stdin>',fact_371_double__eq__0__iff) ).

fof(c_0_466,axiom,
    ! [X3] :
      ( linord219039673up_add(X3)
     => ! [X14] :
          ( zero_zero(X3) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X14),X14)
        <=> ti(X3,X14) = zero_zero(X3) ) ),
    file('<stdin>',fact_336_double__zero__sym) ).

fof(c_0_467,axiom,
    ! [X54,X29] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),X29) = zero_zero(nat)
    <=> ( X54 = zero_zero(nat)
        & X29 = zero_zero(nat) ) ),
    file('<stdin>',fact_327_add__is__0) ).

fof(c_0_468,axiom,
    ! [X51,X53] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),X53) = X51
     => X53 = zero_zero(nat) ),
    file('<stdin>',fact_328_add__eq__self__zero) ).

fof(c_0_469,axiom,
    ! [X3,X80] : hAPP(fun(X3,bool),fun(X3,bool),hAPP(fun(X3,X3),fun(fun(X3,bool),fun(X3,bool)),image(X3,X3),combi(X3)),X80) = ti(fun(X3,bool),X80),
    file('<stdin>',fact_484_image__ident) ).

fof(c_0_470,axiom,
    ! [X53] : hAPP(nat,nat,suc,X53) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),X53),
    file('<stdin>',fact_444_Suc__eq__plus1__left) ).

fof(c_0_471,axiom,
    ! [X53] : hAPP(nat,nat,suc,X53) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X53),one_one(nat)),
    file('<stdin>',fact_445_Suc__eq__plus1) ).

fof(c_0_472,axiom,
    ! [X26] : hAPP(nat,fun(nat,bool),ord_less(nat),X26) = hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X26)),
    file('<stdin>',fact_425_less__eq__Suc__le__raw) ).

fof(c_0_473,axiom,
    ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),top_top(fun(nat,bool)))),
    file('<stdin>',fact_304_infinite__UNIV__nat) ).

fof(c_0_474,axiom,
    ! [X3] : ti(fun(fun(nat,fun(nat,nat)),fun(fun(X3,nat),fun(nat,fun(fun(X3,bool),nat)))),finite_fold_image(nat,X3)) = finite_fold_image(nat,X3),
    file('<stdin>',tsy_c_Finite__Set_Ofold__image_res) ).

fof(c_0_475,axiom,
    ti(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool)),arrow_218898985ctator) = arrow_218898985ctator,
    file('<stdin>',tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_Odictator_res) ).

fof(c_0_476,axiom,
    ti(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),arrow_831799591nimity) = arrow_831799591nimity,
    file('<stdin>',tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_Ounanimity_res) ).

fof(c_0_477,axiom,
    ti(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),arrow_2037941124le_IIA) = arrow_2037941124le_IIA,
    file('<stdin>',tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_OIIA_res) ).

fof(c_0_478,axiom,
    ! [X3] : top_top(fun(X3,bool)) = hAPP(fun(X3,bool),fun(X3,bool),collect(X3),hAPP(bool,fun(X3,bool),combk(bool,X3),fTrue)),
    file('<stdin>',fact_74_UNIV__def) ).

fof(c_0_479,axiom,
    ! [X1,X3,X86,X87] : hAPP(X1,X3,hAPP(X3,fun(X1,X3),combk(X3,X1),X86),X87) = ti(X3,X86),
    file('<stdin>',help_COMBK_1_1_U) ).

fof(c_0_480,axiom,
    ! [X3] :
      ( comm_semiring_1(X3)
     => ! [X21] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),zero_zero(X3)),X21) = ti(X3,X21) ),
    file('<stdin>',fact_436_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).

fof(c_0_481,axiom,
    ! [X3] :
      ( monoid_add(X3)
     => ! [X21] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),zero_zero(X3)),X21) = ti(X3,X21) ),
    file('<stdin>',fact_338_add__0__left) ).

fof(c_0_482,axiom,
    ! [X3] :
      ( comm_monoid_add(X3)
     => ! [X21] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),zero_zero(X3)),X21) = ti(X3,X21) ),
    file('<stdin>',fact_337_add__0) ).

fof(c_0_483,axiom,
    ! [X3] :
      ( comm_semiring_1(X3)
     => ! [X21] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),zero_zero(X3)) = ti(X3,X21) ),
    file('<stdin>',fact_437_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).

fof(c_0_484,axiom,
    ! [X3] :
      ( monoid_add(X3)
     => ! [X21] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),zero_zero(X3)) = ti(X3,X21) ),
    file('<stdin>',fact_335_add__0__right) ).

fof(c_0_485,axiom,
    ! [X3] :
      ( comm_monoid_add(X3)
     => ! [X21] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),zero_zero(X3)) = ti(X3,X21) ),
    file('<stdin>',fact_334_add_Ocomm__neutral) ).

fof(c_0_486,axiom,
    ! [X3,X39] :
      ( ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39))
     => hAPP(fun(X3,bool),nat,finite_card(X3),X39) = zero_zero(nat) ),
    file('<stdin>',fact_356_card__infinite) ).

fof(c_0_487,axiom,
    ti(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),arrow_1322701812_below) = arrow_1322701812_below,
    file('<stdin>',tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_Obelow_res) ).

fof(c_0_488,axiom,
    ti(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),arrow_14103264_above) = arrow_14103264_above,
    file('<stdin>',tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_Oabove_res) ).

fof(c_0_489,axiom,
    ! [X53] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),X53) = X53,
    file('<stdin>',fact_325_plus__nat_Oadd__0) ).

fof(c_0_490,axiom,
    ! [X51] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),zero_zero(nat)) = X51,
    file('<stdin>',fact_326_Nat_Oadd__0__right) ).

fof(c_0_491,axiom,
    ! [X86] :
      ( ~ hBOOL(hAPP(bool,bool,fNot,X86))
      | ~ hBOOL(X86) ),
    file('<stdin>',help_fNot_1_1_U) ).

fof(c_0_492,axiom,
    ! [X67,X68] :
      ( hAPP(nat,nat,suc,X67) = hAPP(nat,nat,suc,X68)
    <=> X67 = X68 ),
    file('<stdin>',fact_385_nat_Oinject) ).

fof(c_0_493,axiom,
    ! [X33,X34] :
      ( hAPP(nat,nat,suc,X33) = hAPP(nat,nat,suc,X34)
     => X33 = X34 ),
    file('<stdin>',fact_384_Suc__inject) ).

fof(c_0_494,axiom,
    ! [X3,X1] : ti(fun(fun(X3,bool),fun(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool))),pi(X3,X1)) = pi(X3,X1),
    file('<stdin>',tsy_c_FuncSet_OPi_res) ).

fof(c_0_495,axiom,
    ! [X2,X3,X4,X5] : ti(X2,hAPP(X3,X2,X4,X5)) = hAPP(X3,X2,X4,X5),
    file('<stdin>',tsy_c_hAPP_res) ).

fof(c_0_496,axiom,
    ! [X3] :
      ( finite_finite(X3)
     => hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),top_top(fun(X3,bool)))) ),
    file('<stdin>',fact_293_finite__UNIV) ).

fof(c_0_497,axiom,
    hBOOL(hAPP(fun(arrow_660593299e_indi,bool),bool,finite_finite_1(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool)))),
    file('<stdin>',fact_277_finite__indi) ).

fof(c_0_498,axiom,
    ! [X3,X1,X2] : ti(fun(fun(X3,fun(X1,X2)),fun(fun(X3,X1),fun(X3,X2))),combs(X3,X1,X2)) = combs(X3,X1,X2),
    file('<stdin>',tsy_c_COMBS_res) ).

fof(c_0_499,axiom,
    ! [X3,X6] : hBOOL(hAPP(X3,bool,top_top(fun(X3,bool)),X6)),
    file('<stdin>',fact_25_top1I) ).

fof(c_0_500,axiom,
    ! [X3,X2,X4,X5] : hAPP(X3,X2,ti(fun(X3,X2),X4),X5) = hAPP(X3,X2,X4,X5),
    file('<stdin>',tsy_c_hAPP_arg1) ).

fof(c_0_501,axiom,
    ! [X3,X1] : ti(fun(fun(X3,bool),fun(fun(X1,bool),fun(sum_sum(X3,X1),bool))),sum_Plus(X3,X1)) = sum_Plus(X3,X1),
    file('<stdin>',tsy_c_Sum__Type_OPlus_res) ).

fof(c_0_502,axiom,
    ! [X3] :
      ( finite_finite(X3)
     => ! [X39] : hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39)) ),
    file('<stdin>',fact_287_finite__code) ).

fof(c_0_503,axiom,
    ! [X3] :
      ( finite_finite(X3)
     => ! [X39] : hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39)) ),
    file('<stdin>',fact_286_finite) ).

fof(c_0_504,axiom,
    ! [X3,X2,X4,X5] : hAPP(X3,X2,X4,ti(X3,X5)) = hAPP(X3,X2,X4,X5),
    file('<stdin>',tsy_c_hAPP_arg2) ).

fof(c_0_505,axiom,
    ! [X1,X2,X3] : ti(fun(fun(X1,fun(X2,X3)),fun(product_prod(X1,X2),X3)),product_prod_rec(X1,X2,X3)) = product_prod_rec(X1,X2,X3),
    file('<stdin>',tsy_c_Product__Type_Oprod_Oprod__rec_res) ).

fof(c_0_506,axiom,
    ! [X3,X1,X2] : ti(fun(fun(X3,fun(X1,X2)),fun(X1,fun(X3,X2))),combc(X3,X1,X2)) = combc(X3,X1,X2),
    file('<stdin>',tsy_c_COMBC_res) ).

fof(c_0_507,axiom,
    ! [X1,X2,X3] : ti(fun(fun(X1,X2),fun(fun(X3,X1),fun(X3,X2))),combb(X1,X2,X3)) = combb(X1,X2,X3),
    file('<stdin>',tsy_c_COMBB_res) ).

fof(c_0_508,axiom,
    ! [X86] :
      ( hBOOL(X86)
      | hBOOL(hAPP(bool,bool,fNot,X86)) ),
    file('<stdin>',help_fNot_2_1_U) ).

fof(c_0_509,axiom,
    ti(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1427655034_mktop) = arrow_1427655034_mktop,
    file('<stdin>',tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_Omktop_res) ).

fof(c_0_510,axiom,
    ti(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1278947948_mkbot) = arrow_1278947948_mkbot,
    file('<stdin>',tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_Omkbot_res) ).

fof(c_0_511,axiom,
    ! [X51] : zero_zero(nat) != hAPP(nat,nat,suc,X51),
    file('<stdin>',fact_424_Zero__not__Suc) ).

fof(c_0_512,axiom,
    ! [X70] : zero_zero(nat) != hAPP(nat,nat,suc,X70),
    file('<stdin>',fact_423_nat_Osimps_I2_J) ).

fof(c_0_513,axiom,
    ! [X51] : hAPP(nat,nat,suc,X51) != zero_zero(nat),
    file('<stdin>',fact_422_Suc__not__Zero) ).

fof(c_0_514,axiom,
    ! [X69] : hAPP(nat,nat,suc,X69) != zero_zero(nat),
    file('<stdin>',fact_421_nat_Osimps_I3_J) ).

fof(c_0_515,axiom,
    ! [X51] : zero_zero(nat) != hAPP(nat,nat,suc,X51),
    file('<stdin>',fact_420_Zero__neq__Suc) ).

fof(c_0_516,axiom,
    ! [X51] : hAPP(nat,nat,suc,X51) != zero_zero(nat),
    file('<stdin>',fact_419_Suc__neq__Zero) ).

fof(c_0_517,axiom,
    ! [X3,X1] : ti(fun(fun(X3,bool),fun(fun(X3,X1),fun(X1,X3))),hilbert_inv_into(X3,X1)) = hilbert_inv_into(X3,X1),
    file('<stdin>',tsy_c_Hilbert__Choice_Oinv__into_res) ).

fof(c_0_518,axiom,
    ! [X53] : X53 != hAPP(nat,nat,suc,X53),
    file('<stdin>',fact_387_n__not__Suc__n) ).

fof(c_0_519,axiom,
    ! [X53] : hAPP(nat,nat,suc,X53) != X53,
    file('<stdin>',fact_386_Suc__n__not__n) ).

fof(c_0_520,axiom,
    ! [X3,X1] : ti(fun(fun(product_prod(X3,X1),bool),fun(X3,fun(X1,bool))),in_rel(X3,X1)) = in_rel(X3,X1),
    file('<stdin>',tsy_c_FunDef_Oin__rel_res) ).

fof(c_0_521,axiom,
    ! [X1,X3] : ti(fun(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool))),image(X1,X3)) = image(X1,X3),
    file('<stdin>',tsy_c_Set_Oimage_res) ).

fof(c_0_522,axiom,
    ! [X3,X11] : hAPP(fun(X3,bool),fun(X3,bool),collect(X3),X11) = ti(fun(X3,bool),X11),
    file('<stdin>',fact_77_Collect__def) ).

fof(c_0_523,axiom,
    ti(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),arrow_1111136790e_Prof) = arrow_1111136790e_Prof,
    file('<stdin>',tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_OProf_res) ).

fof(c_0_524,axiom,
    hAPP(fun(product_unit,bool),nat,finite_card(product_unit),top_top(fun(product_unit,bool))) = one_one(nat),
    file('<stdin>',fact_288_card__UNIV__unit) ).

fof(c_0_525,axiom,
    ! [X1,X3] :
      ( top(X3)
     => ! [X6] : hAPP(X1,X3,top_top(fun(X1,X3)),X6) = top_top(X3) ),
    file('<stdin>',fact_29_top__apply) ).

fof(c_0_526,axiom,
    ! [X3,X1] : ti(fun(fun(X3,X1),fun(fun(X3,bool),bool)),inj_on(X3,X1)) = inj_on(X3,X1),
    file('<stdin>',tsy_c_Fun_Oinj__on_res) ).

fof(c_0_527,axiom,
    ! [X3,X86] : hAPP(X3,X3,combi(X3),X86) = ti(X3,X86),
    file('<stdin>',help_COMBI_1_1_U) ).

fof(c_0_528,axiom,
    ! [X34] :
      ( X34 != zero_zero(nat)
     => ~ ! [X74] : X34 != hAPP(nat,nat,suc,X74) ),
    file('<stdin>',fact_450_nat_Oexhaust) ).

fof(c_0_529,axiom,
    ! [X53] :
      ( X53 != zero_zero(nat)
     => ? [X32] : X53 = hAPP(nat,nat,suc,X32) ),
    file('<stdin>',fact_449_not0__implies__Suc) ).

fof(c_0_530,axiom,
    one_one(nat) = hAPP(nat,nat,suc,zero_zero(nat)),
    file('<stdin>',fact_402_One__nat__def) ).

fof(c_0_531,axiom,
    ! [X3,X1] : ti(fun(X3,fun(X1,product_prod(X3,X1))),product_Pair(X3,X1)) = product_Pair(X3,X1),
    file('<stdin>',tsy_c_Product__Type_OPair_res) ).

fof(c_0_532,axiom,
    ! [X3] : ti(fun(bool,fun(X3,fun(X3,X3))),if(X3)) = if(X3),
    file('<stdin>',tsy_c_If_res) ).

fof(c_0_533,axiom,
    ! [X3] :
      ( linorder(X3)
     => ti(fun(X3,fun(X3,fun(X3,bool))),ord_atLeastLessThan(X3)) = ord_atLeastLessThan(X3) ),
    file('<stdin>',tsy_c_SetInterval_Oord__class_OatLeastLessThan_res) ).

fof(c_0_534,axiom,
    ! [X3] : ti(fun(X3,fun(fun(X3,bool),bool)),member(X3)) = member(X3),
    file('<stdin>',tsy_c_member_res) ).

fof(c_0_535,axiom,
    ti(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),arrow_2064824852le_Lin) = arrow_2064824852le_Lin,
    file('<stdin>',tsy_c_Arrow__Order__Mirabelle__qybrzdpdmn_OLin_res) ).

fof(c_0_536,axiom,
    ! [X3] : ti(fun(fun(X3,bool),fun(X3,bool)),collect(X3)) = collect(X3),
    file('<stdin>',tsy_c_Set_OCollect_res) ).

fof(c_0_537,axiom,
    ! [X3,X1] : ti(fun(X3,fun(X1,X3)),combk(X3,X1)) = combk(X3,X1),
    file('<stdin>',tsy_c_COMBK_res) ).

fof(c_0_538,axiom,
    ! [X3] :
      ( cancel_semigroup_add(X3)
     => ti(fun(X3,fun(X3,X3)),plus_plus(X3)) = plus_plus(X3) ),
    file('<stdin>',tsy_c_Groups_Oplus__class_Oplus_2_res) ).

fof(c_0_539,axiom,
    ! [X3] :
      ( ab_semigroup_add(X3)
     => ti(fun(X3,fun(X3,X3)),plus_plus(X3)) = plus_plus(X3) ),
    file('<stdin>',tsy_c_Groups_Oplus__class_Oplus_1_res) ).

fof(c_0_540,axiom,
    ! [X3] :
      ( monoid_add(X3)
     => ti(fun(X3,fun(X3,X3)),plus_plus(X3)) = plus_plus(X3) ),
    file('<stdin>',tsy_c_Groups_Oplus__class_Oplus_0_res) ).

fof(c_0_541,axiom,
    ! [X1] :
      ( ord(X1)
     => ti(fun(X1,fun(X1,bool)),ord_less_eq(X1)) = ord_less_eq(X1) ),
    file('<stdin>',tsy_c_Orderings_Oord__class_Oless__eq_res) ).

fof(c_0_542,axiom,
    ! [X3] :
      ( ord(X3)
     => ti(fun(X3,fun(X3,bool)),ord_less(X3)) = ord_less(X3) ),
    file('<stdin>',tsy_c_Orderings_Oord__class_Oless_res) ).

fof(c_0_543,axiom,
    ! [X3] : ti(fun(X3,fun(X3,bool)),fequal(X3)) = fequal(X3),
    file('<stdin>',tsy_c_fequal_res) ).

fof(c_0_544,axiom,
    ! [X1] : ti(fun(fun(X1,bool),bool),finite_finite_1(X1)) = finite_finite_1(X1),
    file('<stdin>',tsy_c_Finite__Set_Ofinite_res) ).

fof(c_0_545,axiom,
    ! [X3] : ti(fun(fun(X3,bool),nat),finite_card(X3)) = finite_card(X3),
    file('<stdin>',tsy_c_Finite__Set_Ocard_res) ).

fof(c_0_546,axiom,
    ti(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),lba) = lba,
    file('<stdin>',tsy_v_Lba_____res) ).

fof(c_0_547,axiom,
    ti(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),lab) = lab,
    file('<stdin>',tsy_v_Lab_____res) ).

fof(c_0_548,axiom,
    ti(fun(bool,fun(bool,bool)),fdisj) = fdisj,
    file('<stdin>',tsy_c_fdisj_res) ).

fof(c_0_549,axiom,
    ti(fun(bool,fun(bool,bool)),fconj) = fconj,
    file('<stdin>',tsy_c_fconj_res) ).

fof(c_0_550,axiom,
    ! [X3] :
      ( ring_1(X3)
     => ti(fun(X3,bool),ring_1_Ints(X3)) = ring_1_Ints(X3) ),
    file('<stdin>',tsy_c_Int_Oring__1__class_OInts_res) ).

fof(c_0_551,axiom,
    ! [X3] :
      ( zero(X3)
     => ! [X6] :
          ( zero_zero(X3) = ti(X3,X6)
        <=> ti(X3,X6) = zero_zero(X3) ) ),
    file('<stdin>',fact_331_zero__reorient) ).

fof(c_0_552,axiom,
    ! [X3] :
      ( one(X3)
     => ! [X6] :
          ( one_one(X3) = ti(X3,X6)
        <=> ti(X3,X6) = one_one(X3) ) ),
    file('<stdin>',fact_167_one__reorient) ).

fof(c_0_553,axiom,
    ! [X84,X85] : ti(X84,ti(X84,X85)) = ti(X84,X85),
    file('<stdin>',help_ti_idem) ).

fof(c_0_554,axiom,
    ! [X3] : ti(fun(X3,X3),combi(X3)) = combi(X3),
    file('<stdin>',tsy_c_COMBI_res) ).

fof(c_0_555,axiom,
    ! [X82,X83] :
      ( ( finite_finite(X83)
        & finite_finite(X82) )
     => finite_finite(product_prod(X82,X83)) ),
    file('<stdin>',arity_prod___Finite__Set_Ofinite) ).

fof(c_0_556,axiom,
    ! [X82,X83] :
      ( ( finite_finite(X83)
        & finite_finite(X82) )
     => finite_finite(sum_sum(X82,X83)) ),
    file('<stdin>',arity_sum___Finite__Set_Ofinite) ).

fof(c_0_557,axiom,
    ! [X82,X83] :
      ( ( finite_finite(X83)
        & finite_finite(X82) )
     => finite_finite(fun(X82,X83)) ),
    file('<stdin>',arity_fun___Finite__Set_Ofinite) ).

fof(c_0_558,axiom,
    ! [X82,X83] :
      ( ord(X83)
     => ord(fun(X82,X83)) ),
    file('<stdin>',arity_fun___Orderings_Oord) ).

fof(c_0_559,axiom,
    ! [X82,X83] :
      ( top(X83)
     => top(fun(X82,X83)) ),
    file('<stdin>',arity_fun___Orderings_Otop) ).

fof(c_0_560,axiom,
    ! [X82,X83] :
      ( order(X83)
     => order(fun(X82,X83)) ),
    file('<stdin>',arity_fun___Orderings_Oorder) ).

fof(c_0_561,axiom,
    ! [X82,X83] :
      ( preorder(X83)
     => preorder(fun(X82,X83)) ),
    file('<stdin>',arity_fun___Orderings_Opreorder) ).

fof(c_0_562,axiom,
    ti(fun(arrow_660593299e_indi,nat),h) = h,
    file('<stdin>',tsy_v_h_____res) ).

fof(c_0_563,axiom,
    ti(fun(bool,bool),fNot) = fNot,
    file('<stdin>',tsy_c_fNot_res) ).

fof(c_0_564,axiom,
    ti(fun(nat,nat),suc) = suc,
    file('<stdin>',tsy_c_Nat_OSuc_res) ).

fof(c_0_565,axiom,
    ! [X3] :
      ( top(X3)
     => ti(X3,top_top(X3)) = top_top(X3) ),
    file('<stdin>',tsy_c_Orderings_Otop__class_Otop_res) ).

fof(c_0_566,axiom,
    ! [X3] :
      ( zero(X3)
     => ti(X3,zero_zero(X3)) = zero_zero(X3) ),
    file('<stdin>',tsy_c_Groups_Ozero__class_Ozero_res) ).

fof(c_0_567,axiom,
    ! [X3] :
      ( one(X3)
     => ti(X3,one_one(X3)) = one_one(X3) ),
    file('<stdin>',tsy_c_Groups_Oone__class_Oone_res) ).

fof(c_0_568,axiom,
    ! [X86] :
      ( ti(bool,X86) = fTrue
      | ti(bool,X86) = fFalse ),
    file('<stdin>',help_fTrue_1_1_T) ).

fof(c_0_569,axiom,
    ! [X86] :
      ( ti(bool,X86) = fTrue
      | ti(bool,X86) = fFalse ),
    file('<stdin>',help_If_3_1_T) ).

fof(c_0_570,axiom,
    ! [X3] : ti(X3,undefined(X3)) = undefined(X3),
    file('<stdin>',tsy_c_HOL_Oundefined_res) ).

fof(c_0_571,axiom,
    ! [X3] :
      ( zero_neq_one(X3)
     => one_one(X3) != zero_zero(X3) ),
    file('<stdin>',fact_333_one__neq__zero) ).

fof(c_0_572,axiom,
    ! [X3] :
      ( zero_neq_one(X3)
     => zero_zero(X3) != one_one(X3) ),
    file('<stdin>',fact_332_zero__neq__one) ).

fof(c_0_573,axiom,
    ! [X83] :
      ( finite_finite(X83)
     => finite_finite(option(X83)) ),
    file('<stdin>',arity_Option_Ooption___Finite__Set_Ofinite) ).

fof(c_0_574,axiom,
    ti(nat,n) = n,
    file('<stdin>',tsy_v_n_____res) ).

fof(c_0_575,axiom,
    ti(arrow_490897120le_alt,e) = e,
    file('<stdin>',tsy_v_e_____res) ).

fof(c_0_576,axiom,
    ti(arrow_490897120le_alt,b) = b,
    file('<stdin>',tsy_v_b_____res) ).

fof(c_0_577,axiom,
    ti(arrow_490897120le_alt,a) = a,
    file('<stdin>',tsy_v_a_____res) ).

fof(c_0_578,axiom,
    ti(bool,fTrue) = fTrue,
    file('<stdin>',tsy_c_fTrue_res) ).

fof(c_0_579,axiom,
    ti(bool,fFalse) = fFalse,
    file('<stdin>',tsy_c_fFalse_res) ).

fof(c_0_580,axiom,
    hBOOL(fTrue),
    file('<stdin>',help_fTrue_1_1_U) ).

fof(c_0_581,axiom,
    finite_finite(product_unit),
    file('<stdin>',arity_Product__Type_Ounit___Finite__Set_Ofinite) ).

fof(c_0_582,axiom,
    ord(bool),
    file('<stdin>',arity_HOL_Obool___Orderings_Oord) ).

fof(c_0_583,axiom,
    top(bool),
    file('<stdin>',arity_HOL_Obool___Orderings_Otop) ).

fof(c_0_584,axiom,
    order(bool),
    file('<stdin>',arity_HOL_Obool___Orderings_Oorder) ).

fof(c_0_585,axiom,
    finite_finite(bool),
    file('<stdin>',arity_HOL_Obool___Finite__Set_Ofinite) ).

fof(c_0_586,axiom,
    preorder(bool),
    file('<stdin>',arity_HOL_Obool___Orderings_Opreorder) ).

fof(c_0_587,axiom,
    one(nat),
    file('<stdin>',arity_Nat_Onat___Groups_Oone) ).

fof(c_0_588,axiom,
    zero(nat),
    file('<stdin>',arity_Nat_Onat___Groups_Ozero) ).

fof(c_0_589,axiom,
    ord(nat),
    file('<stdin>',arity_Nat_Onat___Orderings_Oord) ).

fof(c_0_590,axiom,
    order(nat),
    file('<stdin>',arity_Nat_Onat___Orderings_Oorder) ).

fof(c_0_591,axiom,
    monoid_add(nat),
    file('<stdin>',arity_Nat_Onat___Groups_Omonoid__add) ).

fof(c_0_592,axiom,
    linorder(nat),
    file('<stdin>',arity_Nat_Onat___Orderings_Olinorder) ).

fof(c_0_593,axiom,
    preorder(nat),
    file('<stdin>',arity_Nat_Onat___Orderings_Opreorder) ).

fof(c_0_594,axiom,
    zero_neq_one(nat),
    file('<stdin>',arity_Nat_Onat___Rings_Ozero__neq__one) ).

fof(c_0_595,axiom,
    comm_semiring_1(nat),
    file('<stdin>',arity_Nat_Onat___Rings_Ocomm__semiring__1) ).

fof(c_0_596,axiom,
    comm_monoid_add(nat),
    file('<stdin>',arity_Nat_Onat___Groups_Ocomm__monoid__add) ).

fof(c_0_597,axiom,
    ab_semigroup_add(nat),
    file('<stdin>',arity_Nat_Onat___Groups_Oab__semigroup__add) ).

fof(c_0_598,axiom,
    linordered_semidom(nat),
    file('<stdin>',arity_Nat_Onat___Rings_Olinordered__semidom) ).

fof(c_0_599,axiom,
    cancel_semigroup_add(nat),
    file('<stdin>',arity_Nat_Onat___Groups_Ocancel__semigroup__add) ).

fof(c_0_600,axiom,
    cancel146912293up_add(nat),
    file('<stdin>',arity_Nat_Onat___Groups_Ocancel__ab__semigroup__add) ).

fof(c_0_601,axiom,
    ordere216010020id_add(nat),
    file('<stdin>',arity_Nat_Onat___Groups_Oordered__comm__monoid__add) ).

fof(c_0_602,axiom,
    ordere779506340up_add(nat),
    file('<stdin>',arity_Nat_Onat___Groups_Oordered__ab__semigroup__add) ).

fof(c_0_603,axiom,
    ordere236663937imp_le(nat),
    file('<stdin>',arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le) ).

fof(c_0_604,axiom,
    ordere223160158up_add(nat),
    file('<stdin>',arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add) ).

fof(c_0_605,axiom,
    semiri456707255roduct(nat),
    file('<stdin>',arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc) ).

fof(c_0_606,axiom,
    a != b,
    file('<stdin>',fact_36__096a_A_126_061_Ab_096) ).

fof(c_0_607,axiom,
    c != d,
    file('<stdin>',fact_2__096c_A_126_061_Ad_096) ).

fof(c_0_608,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e))))))
  <=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))),lab)),lba)))) ),
    c_0_0 ).

fof(c_0_609,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e))))))
  <=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),lab)),lba)))) ),
    c_0_1 ).

fof(c_0_610,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,p)))
  <=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))))) ),
    c_0_2 ).

fof(c_0_611,axiom,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))))),
    c_0_3 ).

fof(c_0_612,axiom,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))))),
    c_0_4 ).

fof(c_0_613,axiom,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))))),
    c_0_5 ).

fof(c_0_614,axiom,
    hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))),arrow_1111136790e_Prof)),
    c_0_6 ).

fof(c_0_615,plain,
    ~ ! [X44] :
        ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X44),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool)))))
       => ( ! [X32] :
              ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X32),X44))
             => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),X32))),lab)),lba)))) )
         => ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X44),one_one(nat))))),lab)),lba)))) ) ),
    inference(fof_simplification,[status(thm)],[c_0_7]) ).

fof(c_0_616,axiom,
    ? [X44] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X44),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool)))))
      & ! [X32] :
          ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X32),X44))
         => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),X32))),lab)),lba)))) )
      & hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X44),one_one(nat))))),lab)),lba)))) ),
    c_0_8 ).

fof(c_0_617,axiom,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))),lab)),lba)))),
    c_0_9 ).

fof(c_0_618,axiom,
    ! [X32] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X32),n))
     => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),X32))),lab)),lba)))) ),
    c_0_10 ).

fof(c_0_619,axiom,
    ! [X29] : hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),X29))),lab)),lba)),arrow_1111136790e_Prof)),
    c_0_11 ).

fof(c_0_620,axiom,
    ! [X3,X1,X41,X40] :
      ( hBOOL(hAPP(fun(X3,fun(X1,bool)),bool,hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,fun(X1,bool)),bool),ord_less_eq(fun(X3,fun(X1,bool))),hAPP(fun(product_prod(X3,X1),bool),fun(X3,fun(X1,bool)),hAPP(fun(X3,fun(fun(product_prod(X3,X1),bool),fun(X1,bool))),fun(fun(product_prod(X3,X1),bool),fun(X3,fun(X1,bool))),combc(X3,fun(product_prod(X3,X1),bool),fun(X1,bool)),hAPP(fun(X3,fun(X1,fun(fun(product_prod(X3,X1),bool),bool))),fun(X3,fun(fun(product_prod(X3,X1),bool),fun(X1,bool))),hAPP(fun(fun(X1,fun(fun(product_prod(X3,X1),bool),bool)),fun(fun(product_prod(X3,X1),bool),fun(X1,bool))),fun(fun(X3,fun(X1,fun(fun(product_prod(X3,X1),bool),bool))),fun(X3,fun(fun(product_prod(X3,X1),bool),fun(X1,bool)))),combb(fun(X1,fun(fun(product_prod(X3,X1),bool),bool)),fun(fun(product_prod(X3,X1),bool),fun(X1,bool)),X3),combc(X1,fun(product_prod(X3,X1),bool),bool)),hAPP(fun(X3,fun(X1,product_prod(X3,X1))),fun(X3,fun(X1,fun(fun(product_prod(X3,X1),bool),bool))),hAPP(fun(fun(X1,product_prod(X3,X1)),fun(X1,fun(fun(product_prod(X3,X1),bool),bool))),fun(fun(X3,fun(X1,product_prod(X3,X1))),fun(X3,fun(X1,fun(fun(product_prod(X3,X1),bool),bool)))),combb(fun(X1,product_prod(X3,X1)),fun(X1,fun(fun(product_prod(X3,X1),bool),bool)),X3),hAPP(fun(product_prod(X3,X1),fun(fun(product_prod(X3,X1),bool),bool)),fun(fun(X1,product_prod(X3,X1)),fun(X1,fun(fun(product_prod(X3,X1),bool),bool))),combb(product_prod(X3,X1),fun(fun(product_prod(X3,X1),bool),bool),X1),member(product_prod(X3,X1)))),product_Pair(X3,X1)))),X41)),hAPP(fun(product_prod(X3,X1),bool),fun(X3,fun(X1,bool)),hAPP(fun(X3,fun(fun(product_prod(X3,X1),bool),fun(X1,bool))),fun(fun(product_prod(X3,X1),bool),fun(X3,fun(X1,bool))),combc(X3,fun(product_prod(X3,X1),bool),fun(X1,bool)),hAPP(fun(X3,fun(X1,fun(fun(product_prod(X3,X1),bool),bool))),fun(X3,fun(fun(product_prod(X3,X1),bool),fun(X1,bool))),hAPP(fun(fun(X1,fun(fun(product_prod(X3,X1),bool),bool)),fun(fun(product_prod(X3,X1),bool),fun(X1,bool))),fun(fun(X3,fun(X1,fun(fun(product_prod(X3,X1),bool),bool))),fun(X3,fun(fun(product_prod(X3,X1),bool),fun(X1,bool)))),combb(fun(X1,fun(fun(product_prod(X3,X1),bool),bool)),fun(fun(product_prod(X3,X1),bool),fun(X1,bool)),X3),combc(X1,fun(product_prod(X3,X1),bool),bool)),hAPP(fun(X3,fun(X1,product_prod(X3,X1))),fun(X3,fun(X1,fun(fun(product_prod(X3,X1),bool),bool))),hAPP(fun(fun(X1,product_prod(X3,X1)),fun(X1,fun(fun(product_prod(X3,X1),bool),bool))),fun(fun(X3,fun(X1,product_prod(X3,X1))),fun(X3,fun(X1,fun(fun(product_prod(X3,X1),bool),bool)))),combb(fun(X1,product_prod(X3,X1)),fun(X1,fun(fun(product_prod(X3,X1),bool),bool)),X3),hAPP(fun(product_prod(X3,X1),fun(fun(product_prod(X3,X1),bool),bool)),fun(fun(X1,product_prod(X3,X1)),fun(X1,fun(fun(product_prod(X3,X1),bool),bool))),combb(product_prod(X3,X1),fun(fun(product_prod(X3,X1),bool),bool),X1),member(product_prod(X3,X1)))),product_Pair(X3,X1)))),X40)))
    <=> hBOOL(hAPP(fun(product_prod(X3,X1),bool),bool,hAPP(fun(product_prod(X3,X1),bool),fun(fun(product_prod(X3,X1),bool),bool),ord_less_eq(fun(product_prod(X3,X1),bool)),X41),X40)) ),
    c_0_12 ).

fof(c_0_621,axiom,
    ! [X42,X71] :
      ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),X71))
     => hAPP(nat,nat,suc,hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),hAPP(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool)),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool))),combb(nat,fun(fun(nat,bool),bool),nat),member(nat)),suc)),X71))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X42))))) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),X71))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,X42))))) ),
    c_0_13 ).

fof(c_0_622,plain,
    ! [X42,X71] :
      ( ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),X71))
     => hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),hAPP(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool)),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool))),combb(nat,fun(fun(nat,bool),bool),nat),member(nat)),suc)),X71))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X42)))) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),X71))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,X42))))) ),
    inference(fof_simplification,[status(thm)],[c_0_14]) ).

fof(c_0_623,axiom,
    ! [X3,X1] :
      ( ( order(X1)
        & order(X3) )
     => ! [X37,X17,X14,X15] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X14),X15))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X3,X1,X37,X15)),X17))
           => ( ! [X26,X46] :
                  ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X26),X46))
                 => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X3,X1,X37,X26)),hAPP(X3,X1,X37,X46))) )
             => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X3,X1,X37,X14)),X17)) ) ) ) ),
    c_0_15 ).

fof(c_0_624,axiom,
    ! [X3,X1] :
      ( ( order(X1)
        & order(X3) )
     => ! [X37,X17,X14,X15] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X14),X15))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X3,X1,X37,X15)),X17))
           => ( ! [X26,X46] :
                  ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X26),X46))
                 => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X3,X1,X37,X26)),hAPP(X3,X1,X37,X46))) )
             => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X3,X1,X37,X14)),X17)) ) ) ) ),
    c_0_16 ).

fof(c_0_625,axiom,
    ! [X1,X3] :
      ( ( order(X3)
        & order(X1) )
     => ! [X17,X37,X15,X14] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X1,X3,X37,X15)),X14))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X17),X15))
           => ( ! [X26,X46] :
                  ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X46),X26))
                 => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X1,X3,X37,X46)),hAPP(X1,X3,X37,X26))) )
             => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X1,X3,X37,X17)),X14)) ) ) ) ),
    c_0_17 ).

fof(c_0_626,axiom,
    ! [X1,X3] :
      ( ( order(X3)
        & ord(X1) )
     => ! [X17,X37,X15,X14] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X1,X3,X37,X15)),X14))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X17),X15))
           => ( ! [X26,X46] :
                  ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X46),X26))
                 => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X1,X3,X37,X46)),hAPP(X1,X3,X37,X26))) )
             => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X1,X3,X37,X17)),X14)) ) ) ) ),
    c_0_18 ).

fof(c_0_627,axiom,
    ! [X1,X3] :
      ( ( order(X3)
        & order(X1) )
     => ! [X17,X37,X15,X14] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X15),X14))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X17),hAPP(X3,X1,X37,X15)))
           => ( ! [X26,X46] :
                  ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X46),X26))
                 => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X3,X1,X37,X46)),hAPP(X3,X1,X37,X26))) )
             => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X17),hAPP(X3,X1,X37,X14))) ) ) ) ),
    c_0_19 ).

fof(c_0_628,axiom,
    ! [X1,X3] :
      ( ( order(X3)
        & order(X1) )
     => ! [X17,X37,X15,X14] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X15),X14))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X17),hAPP(X3,X1,X37,X15)))
           => ( ! [X26,X46] :
                  ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X46),X26))
                 => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X3,X1,X37,X46)),hAPP(X3,X1,X37,X26))) )
             => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X17),hAPP(X3,X1,X37,X14))) ) ) ) ),
    c_0_20 ).

fof(c_0_629,axiom,
    ! [X3,X1] :
      ( ( order(X1)
        & order(X3) )
     => ! [X17,X14,X37,X15] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X14),hAPP(X1,X3,X37,X15)))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X15),X17))
           => ( ! [X26,X46] :
                  ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X26),X46))
                 => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X1,X3,X37,X26)),hAPP(X1,X3,X37,X46))) )
             => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X14),hAPP(X1,X3,X37,X17))) ) ) ) ),
    c_0_21 ).

fof(c_0_630,axiom,
    ! [X3,X1] :
      ( ( order(X1)
        & order(X3) )
     => ! [X17,X14,X37,X15] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X14),hAPP(X1,X3,X37,X15)))
         => ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X15),X17))
           => ( ! [X26,X46] :
                  ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X26),X46))
                 => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X1,X3,X37,X26)),hAPP(X1,X3,X37,X46))) )
             => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X14),hAPP(X1,X3,X37,X17))) ) ) ) ),
    c_0_22 ).

fof(c_0_631,axiom,
    ! [X10,X11,X12,X13,X14,X15] :
      ( ti(arrow_490897120le_alt,X14) != ti(arrow_490897120le_alt,X15)
     => ( ti(arrow_490897120le_alt,X12) != ti(arrow_490897120le_alt,X13)
       => ( ti(arrow_490897120le_alt,X14) != ti(arrow_490897120le_alt,X13)
         => ( ti(arrow_490897120le_alt,X15) != ti(arrow_490897120le_alt,X12)
           => ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X11),arrow_1111136790e_Prof))
             => ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X10),arrow_1111136790e_Prof))
               => ( ! [X16] :
                      ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X14),X15)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X11,X16)))
                    <=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X12),X13)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X10,X16))) )
                 => ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X14),X15)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X11)))
                   => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X12),X13)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X10))) ) ) ) ) ) ) ) ),
    c_0_23 ).

fof(c_0_632,axiom,
    ! [X10,X11,X12,X13,X14,X15] :
      ( ti(arrow_490897120le_alt,X14) != ti(arrow_490897120le_alt,X15)
     => ( ti(arrow_490897120le_alt,X12) != ti(arrow_490897120le_alt,X13)
       => ( ti(arrow_490897120le_alt,X14) != ti(arrow_490897120le_alt,X13)
         => ( ti(arrow_490897120le_alt,X15) != ti(arrow_490897120le_alt,X12)
           => ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X11),arrow_1111136790e_Prof))
             => ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X10),arrow_1111136790e_Prof))
               => ( ! [X16] :
                      ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X14),X15)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X11,X16)))
                    <=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X12),X13)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X10,X16))) )
                 => ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X14),X15)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X11)))
                  <=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X12),X13)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X10))) ) ) ) ) ) ) ) ),
    c_0_24 ).

fof(c_0_633,axiom,
    ! [X10,X11,X12,X13,X14,X15] :
      ( ti(arrow_490897120le_alt,X14) != ti(arrow_490897120le_alt,X15)
     => ( ti(arrow_490897120le_alt,X12) != ti(arrow_490897120le_alt,X13)
       => ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X11),arrow_1111136790e_Prof))
         => ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X10),arrow_1111136790e_Prof))
           => ( ! [X16] :
                  ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X14),X15)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X11,X16)))
                <=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X12),X13)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X10,X16))) )
             => ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X14),X15)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X11)))
              <=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X12),X13)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X10))) ) ) ) ) ) ),
    c_0_25 ).

fof(c_0_634,axiom,
    ! [X42,X71] :
      ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),X71))
     => hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),X71))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,X42))))) != zero_zero(nat) ),
    c_0_26 ).

fof(c_0_635,plain,
    ! [X16] :
      ( ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X16)),n))
         => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X16)),e))) )
        & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X16)),n))
         => ( ( hAPP(arrow_660593299e_indi,nat,h,X16) = n
             => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X16)),c),e))) )
            & ( hAPP(arrow_660593299e_indi,nat,h,X16) != n
             => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X16)),e))) ) ) ) )
    <=> ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X16)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
         => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab)) )
        & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X16)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
         => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba)) ) ) ),
    inference(fof_simplification,[status(thm)],[c_0_27]) ).

fof(c_0_636,axiom,
    ! [X42,X25] :
      ( hBOOL(hAPP(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X25),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1111136790e_Prof),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_2064824852le_Lin))))
     => ( ! [X26] :
            ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X26),arrow_1111136790e_Prof))
           => ! [X19,X20] :
                ( ti(arrow_490897120le_alt,X19) != ti(arrow_490897120le_alt,X20)
               => ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X19),X20)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X26,X42)))
                 => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X19),X20)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X25,X26))) ) ) )
       => hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,X25),X42)) ) ),
    c_0_28 ).

fof(c_0_637,plain,
    ! [X16] :
      ( ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X16)),n))
         => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X16)),e))) )
        & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X16)),n))
         => ( ( hAPP(arrow_660593299e_indi,nat,h,X16) = n
             => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X16)),c),e))) )
            & ( hAPP(arrow_660593299e_indi,nat,h,X16) != n
             => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X16)),e))) ) ) ) )
    <=> ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X16)),n))
         => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab)) )
        & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X16)),n))
         => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba)) ) ) ),
    inference(fof_simplification,[status(thm)],[c_0_29]) ).

fof(c_0_638,plain,
    ! [X16] :
      ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X16)))
    <=> ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X16)),n))
         => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X16)),e))) )
        & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X16)),n))
         => ( ( hAPP(arrow_660593299e_indi,nat,h,X16) = n
             => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X16)),c),e))) )
            & ( hAPP(arrow_660593299e_indi,nat,h,X16) != n
             => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X16)),e))) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[c_0_30]) ).

fof(c_0_639,axiom,
    ! [X25] :
      ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X25))
    <=> ! [X26] :
          ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X26),arrow_1111136790e_Prof))
         => ! [X27] :
              ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X27),arrow_1111136790e_Prof))
             => ! [X19,X20] :
                  ( ! [X16] :
                      ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X19),X20)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X26,X16)))
                    <=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X19),X20)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X27,X16))) )
                 => ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X19),X20)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X25,X26)))
                  <=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X19),X20)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X25,X27))) ) ) ) ) ),
    c_0_31 ).

fof(c_0_640,axiom,
    ! [X10,X11,X17,X14,X15] :
      ( ti(arrow_490897120le_alt,X14) != ti(arrow_490897120le_alt,X15)
     => ( ti(arrow_490897120le_alt,X15) != ti(arrow_490897120le_alt,X17)
       => ( ti(arrow_490897120le_alt,X14) != ti(arrow_490897120le_alt,X17)
         => ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X11),arrow_1111136790e_Prof))
           => ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X10),arrow_1111136790e_Prof))
             => ( ! [X16] :
                    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X14),X15)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X11,X16)))
                  <=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X15),X17)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X10,X16))) )
               => ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X14),X15)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X11)))
                <=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X15),X17)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X10))) ) ) ) ) ) ) ),
    c_0_32 ).

fof(c_0_641,axiom,
    ! [X3,X11,X50] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),hAPP(fun(X3,bool),fun(X3,bool),collect(X3),hAPP(fun(X3,bool),fun(X3,bool),hAPP(fun(X3,fun(bool,bool)),fun(fun(X3,bool),fun(X3,bool)),combs(X3,bool,bool),hAPP(fun(X3,bool),fun(X3,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X3,bool),fun(X3,fun(bool,bool))),combb(bool,fun(bool,bool),X3),fdisj),X11)),X50))))
    <=> ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),hAPP(fun(X3,bool),fun(X3,bool),collect(X3),X11)))
        & hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),hAPP(fun(X3,bool),fun(X3,bool),collect(X3),X50))) ) ),
    c_0_33 ).

fof(c_0_642,axiom,
    ! [X10,X11,X14,X15] :
      ( ti(arrow_490897120le_alt,X14) != ti(arrow_490897120le_alt,X15)
     => ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X11),arrow_1111136790e_Prof))
       => ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X10),arrow_1111136790e_Prof))
         => ( ! [X16] :
                ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X14),X15)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X11,X16)))
              <=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X15),X14)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X10,X16))) )
           => ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X14),X15)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X11)))
            <=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X15),X14)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X10))) ) ) ) ) ),
    c_0_34 ).

fof(c_0_643,axiom,
    ! [X11,X42] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),X11)),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X42))))),
    c_0_35 ).

fof(c_0_644,axiom,
    ! [X6,X7,X8,X14,X15] :
      ( ti(arrow_490897120le_alt,X14) != ti(arrow_490897120le_alt,X15)
     => ( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X8),arrow_2064824852le_Lin))
       => ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X6),X7)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X8),X14),X15)))
        <=> ( ti(arrow_490897120le_alt,X6) != ti(arrow_490897120le_alt,X7)
            & ( ti(arrow_490897120le_alt,X7) = ti(arrow_490897120le_alt,X14)
             => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X6),X15)),X8)) )
            & ( ti(arrow_490897120le_alt,X7) != ti(arrow_490897120le_alt,X14)
             => ( ( ti(arrow_490897120le_alt,X6) = ti(arrow_490897120le_alt,X14)
                 => ( ti(arrow_490897120le_alt,X7) = ti(arrow_490897120le_alt,X15)
                    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X15),X7)),X8)) ) )
                & ( ti(arrow_490897120le_alt,X6) != ti(arrow_490897120le_alt,X14)
                 => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X6),X7)),X8)) ) ) ) ) ) ) ),
    c_0_36 ).

fof(c_0_645,axiom,
    ! [X6,X7,X8,X14,X15] :
      ( ti(arrow_490897120le_alt,X14) != ti(arrow_490897120le_alt,X15)
     => ( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X8),arrow_2064824852le_Lin))
       => ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X6),X7)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X8),X14),X15)))
        <=> ( ti(arrow_490897120le_alt,X6) != ti(arrow_490897120le_alt,X7)
            & ( ti(arrow_490897120le_alt,X6) = ti(arrow_490897120le_alt,X15)
             => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X14),X7)),X8)) )
            & ( ti(arrow_490897120le_alt,X6) != ti(arrow_490897120le_alt,X15)
             => ( ( ti(arrow_490897120le_alt,X7) = ti(arrow_490897120le_alt,X15)
                 => ( ti(arrow_490897120le_alt,X6) = ti(arrow_490897120le_alt,X14)
                    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X6),X14)),X8)) ) )
                & ( ti(arrow_490897120le_alt,X7) != ti(arrow_490897120le_alt,X15)
                 => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X6),X7)),X8)) ) ) ) ) ) ) ),
    c_0_37 ).

fof(c_0_646,axiom,
    ! [X1,X3,X43,X49,X39] :
      ( ! [X26] :
          ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X26),X39))
         => hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(X3,fun(X1,bool),X43,X26)),hAPP(X3,fun(X1,bool),X49,X26))) )
     => hBOOL(hAPP(fun(fun(X3,X1),bool),bool,hAPP(fun(fun(X3,X1),bool),fun(fun(fun(X3,X1),bool),bool),ord_less_eq(fun(fun(X3,X1),bool)),hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool)),pi(X3,X1),X39),X43)),hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool)),pi(X3,X1),X39),X49))) ),
    c_0_38 ).

fof(c_0_647,axiom,
    ! [X1,X3,X43,X37,X38,X39] :
      ( ! [X47] :
          ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X47),X39))
         => hAPP(X3,X1,X37,X47) = hAPP(X3,X1,X38,X47) )
     => ( hBOOL(hAPP(fun(fun(X3,X1),bool),bool,hAPP(fun(X3,X1),fun(fun(fun(X3,X1),bool),bool),member(fun(X3,X1)),X37),hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool)),pi(X3,X1),X39),X43)))
      <=> hBOOL(hAPP(fun(fun(X3,X1),bool),bool,hAPP(fun(X3,X1),fun(fun(fun(X3,X1),bool),bool),member(fun(X3,X1)),X38),hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool)),pi(X3,X1),X39),X43))) ) ),
    c_0_39 ).

fof(c_0_648,axiom,
    ! [X3,X1,X40,X41] :
      ( ! [X26,X27] :
          ( hBOOL(hAPP(fun(product_prod(X3,X1),bool),bool,hAPP(product_prod(X3,X1),fun(fun(product_prod(X3,X1),bool),bool),member(product_prod(X3,X1)),hAPP(X1,product_prod(X3,X1),hAPP(X3,fun(X1,product_prod(X3,X1)),product_Pair(X3,X1),X26),X27)),X41))
        <=> hBOOL(hAPP(fun(product_prod(X3,X1),bool),bool,hAPP(product_prod(X3,X1),fun(fun(product_prod(X3,X1),bool),bool),member(product_prod(X3,X1)),hAPP(X1,product_prod(X3,X1),hAPP(X3,fun(X1,product_prod(X3,X1)),product_Pair(X3,X1),X26),X27)),X40)) )
    <=> ti(fun(product_prod(X3,X1),bool),X41) = ti(fun(product_prod(X3,X1),bool),X40) ),
    c_0_40 ).

fof(c_0_649,axiom,
    hBOOL(hAPP(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),f),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1111136790e_Prof),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_2064824852le_Lin)))),
    c_0_41 ).

fof(c_0_650,axiom,
    ! [X3,X50,X11] :
      ( ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),hAPP(fun(X3,bool),fun(X3,bool),collect(X3),X11)))
        | hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),hAPP(fun(X3,bool),fun(X3,bool),collect(X3),X50))) )
     => hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),hAPP(fun(X3,bool),fun(X3,bool),collect(X3),hAPP(fun(X3,bool),fun(X3,bool),hAPP(fun(X3,fun(bool,bool)),fun(fun(X3,bool),fun(X3,bool)),combs(X3,bool,bool),hAPP(fun(X3,bool),fun(X3,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X3,bool),fun(X3,fun(bool,bool))),combb(bool,fun(bool,bool),X3),fconj),X11)),X50)))) ),
    c_0_42 ).

fof(c_0_651,axiom,
    ! [X66,X37] :
      ( ! [X44] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X44),hAPP(nat,nat,X37,X44)))
     => hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less_eq(nat)),X37)),X66)))) ),
    c_0_43 ).

fof(c_0_652,axiom,
    ! [X1,X3,X37,X43,X39] :
      ( ! [X26] :
          ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X26),X39))
         => hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X3,X1,X37,X26)),hAPP(X3,fun(X1,bool),X43,X26))) )
     => hBOOL(hAPP(fun(fun(X3,X1),bool),bool,hAPP(fun(X3,X1),fun(fun(fun(X3,X1),bool),bool),member(fun(X3,X1)),X37),hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool)),pi(X3,X1),X39),X43))) ),
    c_0_44 ).

fof(c_0_653,axiom,
    ! [X1,X3,X37,X43,X39] :
      ( ! [X26] :
          ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X26),X39))
         => hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X3,X1,X37,X26)),hAPP(X3,fun(X1,bool),X43,X26))) )
     => hBOOL(hAPP(fun(fun(X3,X1),bool),bool,hAPP(fun(X3,X1),fun(fun(fun(X3,X1),bool),bool),member(fun(X3,X1)),X37),hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool)),pi(X3,X1),X39),X43))) ),
    c_0_45 ).

fof(c_0_654,axiom,
    ! [X3] :
      ( linordered_idom(X3)
     => ! [X14] :
          ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X14),ring_1_Ints(X3)))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),one_one(X3)),X14)),X14)),zero_zero(X3)))
          <=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X14),zero_zero(X3))) ) ) ),
    c_0_46 ).

fof(c_0_655,axiom,
    ! [X1,X3,X43,X39,X37,X9,X38,X25] :
      ( hBOOL(hAPP(fun(fun(X1,bool),X3),bool,hAPP(fun(X1,X3),fun(fun(fun(X1,bool),X3),bool),hAPP(X3,fun(fun(X1,X3),fun(fun(fun(X1,bool),X3),bool)),hAPP(fun(X3,fun(X3,X3)),fun(X3,fun(fun(X1,X3),fun(fun(fun(X1,bool),X3),bool))),finite908156982e_idem(X3,X1),X37),X9),X38),X25))
     => ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X39))
       => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X43),X39))
         => hAPP(X3,X3,hAPP(X3,fun(X3,X3),X37,hAPP(fun(X1,bool),X3,X25,X43)),hAPP(fun(X1,bool),X3,X25,X39)) = hAPP(fun(X1,bool),X3,X25,X39) ) ) ),
    c_0_47 ).

fof(c_0_656,axiom,
    ! [X1,X3,X37,X43,X39] :
      ( ! [X26] :
          ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X26),X39))
         => hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X3,X1,X37,X26)),X43)) )
     => hBOOL(hAPP(fun(fun(X3,X1),bool),bool,hAPP(fun(X3,X1),fun(fun(fun(X3,X1),bool),bool),member(fun(X3,X1)),X37),hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool)),pi(X3,X1),X39),hAPP(fun(X1,bool),fun(X3,fun(X1,bool)),combk(fun(X1,bool),X3),X43)))) ),
    c_0_48 ).

fof(c_0_657,axiom,
    ! [X1,X3,X6,X39,X37,X9,X38,X25] :
      ( hBOOL(hAPP(fun(fun(X1,bool),X3),bool,hAPP(fun(X1,X3),fun(fun(fun(X1,bool),X3),bool),hAPP(X3,fun(fun(X1,X3),fun(fun(fun(X1,bool),X3),bool)),hAPP(fun(X3,fun(X3,X3)),fun(X3,fun(fun(X1,X3),fun(fun(fun(X1,bool),X3),bool))),finite908156982e_idem(X3,X1),X37),X9),X38),X25))
     => ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X39))
       => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X39))
         => hAPP(X3,X3,hAPP(X3,fun(X3,X3),X37,hAPP(X1,X3,X38,X6)),hAPP(fun(X1,bool),X3,X25,X39)) = hAPP(fun(X1,bool),X3,X25,X39) ) ) ),
    c_0_49 ).

fof(c_0_658,axiom,
    ! [X3,X1,X38,X37,X39,X43] :
      ( hBOOL(hAPP(fun(fun(X3,X1),bool),bool,hAPP(fun(X3,X1),fun(fun(fun(X3,X1),bool),bool),member(fun(X3,X1)),X37),hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool)),pi(X3,X1),X39),hAPP(fun(X1,bool),fun(X3,fun(X1,bool)),combk(fun(X1,bool),X3),X43))))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),X39))
       => ( hBOOL(hAPP(fun(fun(X1,X3),bool),bool,hAPP(fun(X1,X3),fun(fun(fun(X1,X3),bool),bool),member(fun(X1,X3)),X38),hAPP(fun(X1,fun(X3,bool)),fun(fun(X1,X3),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X3,bool)),fun(fun(X1,X3),bool)),pi(X1,X3),X43),hAPP(fun(X3,bool),fun(X1,fun(X3,bool)),combk(fun(X3,bool),X1),X39))))
         => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X38),X43))
           => ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39))
             => ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43))
               => hAPP(fun(X3,bool),nat,finite_card(X3),X39) = hAPP(fun(X1,bool),nat,finite_card(X1),X43) ) ) ) ) ) ),
    c_0_50 ).

fof(c_0_659,axiom,
    ! [X25] :
      ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,X25))
    <=> ! [X26] :
          ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X26),arrow_1111136790e_Prof))
         => ! [X19,X20] :
              ( ! [X16] : hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X19),X20)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X26,X16)))
             => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X19),X20)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X25,X26))) ) ) ),
    c_0_51 ).

fof(c_0_660,axiom,
    ! [X1,X3,X6,X37,X9,X38,X25] :
      ( hBOOL(hAPP(fun(fun(X1,bool),X3),bool,hAPP(fun(X1,X3),fun(fun(fun(X1,bool),X3),bool),hAPP(X3,fun(fun(X1,X3),fun(fun(fun(X1,bool),X3),bool)),hAPP(fun(X3,fun(X3,X3)),fun(X3,fun(fun(X1,X3),fun(fun(fun(X1,bool),X3),bool))),finite908156982e_idem(X3,X1),X37),X9),X38),X25))
     => hAPP(X3,X3,hAPP(X3,fun(X3,X3),X37,X6),X6) = ti(X3,X6) ),
    c_0_52 ).

fof(c_0_661,plain,
    ! [X3,X1,X37,X39] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X3,bool),nat,finite_card(X3),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X37),X39))),hAPP(fun(X1,bool),nat,finite_card(X1),X39)))
     => ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X37),X39)) ),
    inference(fof_simplification,[status(thm)],[c_0_53]) ).

fof(c_0_662,axiom,
    ! [X8,X6,X7] :
      ( ti(arrow_490897120le_alt,X6) != ti(arrow_490897120le_alt,X7)
     => ( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X8),arrow_2064824852le_Lin))
       => hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X8),X6),X7)),arrow_2064824852le_Lin)) ) ),
    c_0_54 ).

fof(c_0_663,axiom,
    ! [X8,X6,X7] :
      ( ti(arrow_490897120le_alt,X6) != ti(arrow_490897120le_alt,X7)
     => ( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X8),arrow_2064824852le_Lin))
       => hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X8),X6),X7)),arrow_2064824852le_Lin)) ) ),
    c_0_55 ).

fof(c_0_664,plain,
    ! [X6,X7,X8] :
      ( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X8),arrow_2064824852le_Lin))
     => ( ti(arrow_490897120le_alt,X6) != ti(arrow_490897120le_alt,X7)
       => ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X6),X7)),X8))
        <=> hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X7),X6)),X8)) ) ) ),
    inference(fof_simplification,[status(thm)],[c_0_56]) ).

fof(c_0_665,plain,
    ! [X14,X15,X8] :
      ( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X8),arrow_2064824852le_Lin))
     => ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X14),X15)),X8))
       => ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X15),X14)),X8)) ) ),
    inference(fof_simplification,[status(thm)],[c_0_57]) ).

fof(c_0_666,axiom,
    ! [X3,X41,X40] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),hAPP(fun(X3,bool),fun(X3,bool),hAPP(fun(X3,fun(fun(X3,bool),bool)),fun(fun(X3,bool),fun(X3,bool)),combc(X3,fun(X3,bool),bool),member(X3)),X41)),hAPP(fun(X3,bool),fun(X3,bool),hAPP(fun(X3,fun(fun(X3,bool),bool)),fun(fun(X3,bool),fun(X3,bool)),combc(X3,fun(X3,bool),bool),member(X3)),X40)))
    <=> hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X41),X40)) ),
    c_0_58 ).

fof(c_0_667,axiom,
    ! [X2,X3,X1,X37,X38] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X38),top_top(fun(X1,bool)))))
     => hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),combb(X3,X2,X1),X37),X38)),top_top(fun(X1,bool))))) ),
    c_0_59 ).

fof(c_0_668,axiom,
    ! [X6,X7,X8,X9] :
      ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X6),X7)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X8),X9)))
    <=> ( ti(arrow_490897120le_alt,X6) != ti(arrow_490897120le_alt,X9)
        & ( ti(arrow_490897120le_alt,X7) = ti(arrow_490897120le_alt,X9)
         => ti(arrow_490897120le_alt,X6) != ti(arrow_490897120le_alt,X7) )
        & ( ti(arrow_490897120le_alt,X7) != ti(arrow_490897120le_alt,X9)
         => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X6),X7)),X8)) ) ) ),
    c_0_60 ).

fof(c_0_669,axiom,
    ! [X6,X7,X8,X9] :
      ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X6),X7)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X8),X9)))
    <=> ( ti(arrow_490897120le_alt,X7) != ti(arrow_490897120le_alt,X9)
        & ( ti(arrow_490897120le_alt,X6) = ti(arrow_490897120le_alt,X9)
         => ti(arrow_490897120le_alt,X6) != ti(arrow_490897120le_alt,X7) )
        & ( ti(arrow_490897120le_alt,X6) != ti(arrow_490897120le_alt,X9)
         => hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X6),X7)),X8)) ) ) ),
    c_0_61 ).

fof(c_0_670,axiom,
    ! [X3,X1,X6,X37,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X37),X39)))
     => hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X3,X1,hAPP(fun(X1,X3),fun(X3,X1),hAPP(fun(X1,bool),fun(fun(X1,X3),fun(X3,X1)),hilbert_inv_into(X1,X3),X39),X37),X6)),X39)) ),
    c_0_62 ).

fof(c_0_671,axiom,
    ! [X54,X57,X37] :
      ( ! [X32,X44] :
          ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X32),X44))
         => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,X37,X32)),hAPP(nat,nat,X37,X44))) )
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,X37,X54)),X57)),hAPP(nat,nat,X37,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),X57)))) ),
    c_0_63 ).

fof(c_0_672,axiom,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,hAPP(nat,arrow_660593299e_indi,hAPP(fun(arrow_660593299e_indi,nat),fun(nat,arrow_660593299e_indi),hAPP(fun(arrow_660593299e_indi,bool),fun(fun(arrow_660593299e_indi,nat),fun(nat,arrow_660593299e_indi)),hilbert_inv_into(arrow_660593299e_indi,nat),top_top(fun(arrow_660593299e_indi,bool))),h),n)))),
    c_0_64 ).

fof(c_0_673,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X29,X54,X37] :
          ( ! [X44] : hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(nat,X3,X37,X44)),hAPP(nat,X3,X37,hAPP(nat,nat,suc,X44))))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(nat,X3,X37,X29)),hAPP(nat,X3,X37,X54)))
          <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X29),X54)) ) ) ),
    c_0_65 ).

fof(c_0_674,axiom,
    ! [X3,X1,X37,X39,X43] :
      ( hBOOL(hAPP(fun(fun(X3,X1),bool),bool,hAPP(fun(X3,X1),fun(fun(fun(X3,X1),bool),bool),member(fun(X3,X1)),X37),hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool)),pi(X3,X1),X39),hAPP(fun(X1,bool),fun(X3,fun(X1,bool)),combk(fun(X1,bool),X3),X43))))
     => hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X37),X39)),X43)) ),
    c_0_66 ).

fof(c_0_675,axiom,
    ! [X3,X1,X39,X43,X37] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),top_top(fun(X3,bool))))
     => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X37),X39)),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X37),X43)))
      <=> hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43)) ) ),
    c_0_67 ).

fof(c_0_676,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X29,X72,X37] :
          ( ! [X44] : hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(nat,X3,X37,X44)),hAPP(nat,X3,X37,hAPP(nat,nat,suc,X44))))
         => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X29),X72))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(nat,X3,X37,X29)),hAPP(nat,X3,X37,X72))) ) ) ),
    c_0_68 ).

fof(c_0_677,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X29,X72,X37] :
          ( ! [X44] : hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(nat,X3,X37,X44)),hAPP(nat,X3,X37,hAPP(nat,nat,suc,X44))))
         => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X29),X72))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(nat,X3,X37,X29)),hAPP(nat,X3,X37,X72))) ) ) ),
    c_0_69 ).

fof(c_0_678,axiom,
    ! [X39,X57] :
      ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),X39),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X57),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X57),hAPP(fun(nat,bool),nat,finite_card(nat),X39)))))
     => X39 = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X57),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X57),hAPP(fun(nat,bool),nat,finite_card(nat),X39))) ),
    c_0_70 ).

fof(c_0_679,axiom,
    ! [X3,X1,X37,X39,X43] :
      ( hBOOL(hAPP(fun(fun(X3,X1),bool),bool,hAPP(fun(X3,X1),fun(fun(fun(X3,X1),bool),bool),member(fun(X3,X1)),X37),hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool)),pi(X3,X1),X39),hAPP(fun(X1,bool),fun(X3,fun(X1,bool)),combk(fun(X1,bool),X3),X43))))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),X39))
       => ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43))
         => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X3,bool),nat,finite_card(X3),X39)),hAPP(fun(X1,bool),nat,finite_card(X1),X43))) ) ) ),
    c_0_71 ).

fof(c_0_680,axiom,
    ! [X1,X3,X39,X37,X6,X7] :
      ( hAPP(X1,X3,hAPP(fun(X3,X1),fun(X1,X3),hAPP(fun(X3,bool),fun(fun(X3,X1),fun(X1,X3)),hilbert_inv_into(X3,X1),X39),X37),X6) = hAPP(X1,X3,hAPP(fun(X3,X1),fun(X1,X3),hAPP(fun(X3,bool),fun(fun(X3,X1),fun(X1,X3)),hilbert_inv_into(X3,X1),X39),X37),X7)
     => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X37),X39)))
       => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X7),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X37),X39)))
         => ti(X1,X6) = ti(X1,X7) ) ) ),
    c_0_72 ).

fof(c_0_681,axiom,
    ! [X3,X1,X6,X37,X39,X43] :
      ( hBOOL(hAPP(fun(fun(X3,X1),bool),bool,hAPP(fun(X3,X1),fun(fun(fun(X3,X1),bool),bool),member(fun(X3,X1)),X37),hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool)),pi(X3,X1),X39),hAPP(fun(X1,bool),fun(X3,fun(X1,bool)),combk(fun(X1,bool),X3),X43))))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X39))
       => hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X3,X1,X37,X6)),X43)) ) ),
    c_0_73 ).

fof(c_0_682,axiom,
    ! [X1,X3,X43,X48,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X48),X39))
     => hBOOL(hAPP(fun(fun(X3,X1),bool),bool,hAPP(fun(fun(X3,X1),bool),fun(fun(fun(X3,X1),bool),bool),ord_less_eq(fun(fun(X3,X1),bool)),hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool)),pi(X3,X1),X39),X43)),hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool)),pi(X3,X1),X48),X43))) ),
    c_0_74 ).

fof(c_0_683,axiom,
    ! [X3] :
      ( linorder(X3)
     => ! [X14,X15,X17,X79] :
          ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),hAPP(X3,fun(X3,bool),hAPP(X3,fun(X3,fun(X3,bool)),ord_atLeastLessThan(X3),X14),X15)),hAPP(X3,fun(X3,bool),hAPP(X3,fun(X3,fun(X3,bool)),ord_atLeastLessThan(X3),X17),X79)))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X15),X14))
            | ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X17),X14))
              & hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X15),X79)) ) ) ) ),
    c_0_75 ).

fof(c_0_684,axiom,
    ! [X1,X3,X37,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X37),X39))),hAPP(fun(X3,bool),nat,finite_card(X3),X39))) ),
    c_0_76 ).

fof(c_0_685,axiom,
    ! [X3,X37,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),hAPP(fun(X3,bool),fun(X3,bool),hAPP(fun(X3,X3),fun(fun(X3,bool),fun(X3,bool)),image(X3,X3),X37),X39)),X39))
       => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X3),fun(fun(X3,bool),bool),inj_on(X3,X3),X37),X39))
         => hAPP(fun(X3,bool),fun(X3,bool),hAPP(fun(X3,X3),fun(fun(X3,bool),fun(X3,bool)),image(X3,X3),X37),X39) = ti(fun(X3,bool),X39) ) ) ),
    c_0_77 ).

fof(c_0_686,axiom,
    ! [X3,X1,X6,X37,X39,X43] :
      ( hBOOL(hAPP(fun(fun(X3,X1),bool),bool,hAPP(fun(X3,X1),fun(fun(fun(X3,X1),bool),bool),member(fun(X3,X1)),X37),hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool)),pi(X3,X1),X39),X43)))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X39))
       => hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X3,X1,X37,X6)),hAPP(X3,fun(X1,bool),X43,X6))) ) ),
    c_0_78 ).

fof(c_0_687,plain,
    ! [X3,X1,X6,X37,X39,X43] :
      ( hBOOL(hAPP(fun(fun(X3,X1),bool),bool,hAPP(fun(X3,X1),fun(fun(fun(X3,X1),bool),bool),member(fun(X3,X1)),X37),hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool)),pi(X3,X1),X39),X43)))
     => ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X3,X1,X37,X6)),hAPP(X3,fun(X1,bool),X43,X6)))
       => ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X39)) ) ),
    inference(fof_simplification,[status(thm)],[c_0_79]) ).

fof(c_0_688,axiom,
    ! [X3,X1,X43,X37,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X43),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X37),X39)))
    <=> ? [X81] :
          ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X81),X39))
          & ti(fun(X3,bool),X43) = hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X37),X81) ) ),
    c_0_80 ).

fof(c_0_689,axiom,
    ! [X3,X1,X39,X37,X43] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),X43))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less(fun(X3,bool)),X39),X43))
       => hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X37),X39)),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X37),X43))) ) ),
    c_0_81 ).

fof(c_0_690,axiom,
    ! [X3,X11] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),hAPP(fun(X3,bool),fun(X3,bool),collect(X3),X11)))
     => ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),hAPP(fun(X3,bool),fun(X3,bool),collect(X3),hAPP(fun(X3,bool),fun(X3,bool),hAPP(fun(bool,bool),fun(fun(X3,bool),fun(X3,bool)),combb(bool,bool,X3),fNot),X11))))
      <=> hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),top_top(fun(X3,bool)))) ) ),
    c_0_82 ).

fof(c_0_691,axiom,
    ! [X3,X1,X9,X37,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X9),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X37),X39)))
    <=> ? [X26] :
          ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X26),X39))
          & ti(X3,X9) = hAPP(X1,X3,X37,X26) ) ),
    c_0_83 ).

fof(c_0_692,axiom,
    ! [X1,X3,X41,X6,X7] :
      ( hBOOL(hAPP(X1,bool,hAPP(X3,fun(X1,bool),hAPP(fun(product_prod(X3,X1),bool),fun(X3,fun(X1,bool)),in_rel(X3,X1),X41),X6),X7))
    <=> hBOOL(hAPP(fun(product_prod(X3,X1),bool),bool,hAPP(product_prod(X3,X1),fun(fun(product_prod(X3,X1),bool),bool),member(product_prod(X3,X1)),hAPP(X1,product_prod(X3,X1),hAPP(X3,fun(X1,product_prod(X3,X1)),product_Pair(X3,X1),X6),X7)),X41)) ),
    c_0_84 ).

fof(c_0_693,axiom,
    ! [X3,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39))
     => hBOOL(hAPP(fun(fun(X3,bool),bool),bool,finite_finite_1(fun(X3,bool)),hAPP(fun(fun(X3,bool),bool),fun(fun(X3,bool),bool),collect(fun(X3,bool)),hAPP(fun(X3,bool),fun(fun(X3,bool),bool),hAPP(fun(fun(X3,bool),fun(fun(X3,bool),bool)),fun(fun(X3,bool),fun(fun(X3,bool),bool)),combc(fun(X3,bool),fun(X3,bool),bool),ord_less_eq(fun(X3,bool))),X39)))) ),
    c_0_85 ).

fof(c_0_694,axiom,
    ! [X2,X3,X1,X37] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),top_top(fun(X3,bool))))
     => hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,fun(X2,X1)),fun(fun(X3,bool),bool),inj_on(X3,fun(X2,X1)),hAPP(fun(X3,X1),fun(X3,fun(X2,X1)),hAPP(fun(X1,fun(X2,X1)),fun(fun(X3,X1),fun(X3,fun(X2,X1))),combb(X1,fun(X2,X1),X3),combk(X1,X2)),X37)),top_top(fun(X3,bool)))) ),
    c_0_86 ).

fof(c_0_695,axiom,
    ! [X6,X8] :
      ( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X8),arrow_2064824852le_Lin))
     => hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X8),X6)),arrow_2064824852le_Lin)) ),
    c_0_87 ).

fof(c_0_696,axiom,
    ! [X6,X8] :
      ( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X8),arrow_2064824852le_Lin))
     => hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X8),X6)),arrow_2064824852le_Lin)) ),
    c_0_88 ).

fof(c_0_697,axiom,
    ! [X3] :
      ( ordere236663937imp_le(X3)
     => ! [X14,X17,X15] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X14),X17)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X15),X17)))
        <=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X14),X15)) ) ),
    c_0_89 ).

fof(c_0_698,axiom,
    ! [X3] :
      ( ordere236663937imp_le(X3)
     => ! [X17,X14,X15] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X17),X14)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X17),X15)))
        <=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X14),X15)) ) ),
    c_0_90 ).

fof(c_0_699,axiom,
    ! [X3] :
      ( ordere236663937imp_le(X3)
     => ! [X21,X36,X22] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X36)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X22),X36)))
         => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X22)) ) ),
    c_0_91 ).

fof(c_0_700,axiom,
    ! [X3] :
      ( ordere236663937imp_le(X3)
     => ! [X36,X21,X22] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X36),X21)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X36),X22)))
         => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X22)) ) ),
    c_0_92 ).

fof(c_0_701,axiom,
    ! [X3] :
      ( ordere236663937imp_le(X3)
     => ! [X14,X17,X15] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X14),X17)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X15),X17)))
        <=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X14),X15)) ) ),
    c_0_93 ).

fof(c_0_702,axiom,
    ! [X3] :
      ( ordere236663937imp_le(X3)
     => ! [X17,X14,X15] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X17),X14)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X17),X15)))
        <=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X14),X15)) ) ),
    c_0_94 ).

fof(c_0_703,axiom,
    ! [X3] :
      ( ordere236663937imp_le(X3)
     => ! [X21,X36,X22] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X36)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X22),X36)))
         => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X21),X22)) ) ),
    c_0_95 ).

fof(c_0_704,axiom,
    ! [X3] :
      ( ordere236663937imp_le(X3)
     => ! [X36,X21,X22] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X36),X21)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X36),X22)))
         => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X21),X22)) ) ),
    c_0_96 ).

fof(c_0_705,axiom,
    ! [X1,X3,X37,X39,X43] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43))
     => hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X37),X39)),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X37),X43))) ),
    c_0_97 ).

fof(c_0_706,axiom,
    ! [X57,X54,X29] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X57),X54)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X57),X29)))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X29)) ),
    c_0_98 ).

fof(c_0_707,axiom,
    ! [X57,X54,X29] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X57),X54)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X57),X29)))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X29)) ),
    c_0_99 ).

fof(c_0_708,axiom,
    ! [X3,X1] :
      ( ord(X1)
     => ! [X37,X38] :
          ( ! [X26] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X3,X1,X37,X26)),hAPP(X3,X1,X38,X26)))
         => hBOOL(hAPP(fun(X3,X1),bool,hAPP(fun(X3,X1),fun(fun(X3,X1),bool),ord_less_eq(fun(X3,X1)),X37),X38)) ) ),
    c_0_100 ).

fof(c_0_709,axiom,
    ! [X3,X1] :
      ( ord(X1)
     => ! [X37,X38] :
          ( hBOOL(hAPP(fun(X3,X1),bool,hAPP(fun(X3,X1),fun(fun(X3,X1),bool),ord_less_eq(fun(X3,X1)),X37),X38))
        <=> ! [X26] : hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X3,X1,X37,X26)),hAPP(X3,X1,X38,X26))) ) ),
    c_0_101 ).

fof(c_0_710,axiom,
    ! [X8] :
      ( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X8),arrow_2064824852le_Lin))
     => hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),combk(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),arrow_660593299e_indi),X8)),arrow_1111136790e_Prof)) ),
    c_0_102 ).

fof(c_0_711,axiom,
    ! [X1,X3,X37,X38,X39] :
      ( ! [X19] :
          ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X19),X39))
         => hAPP(X3,X1,X37,X19) = hAPP(X3,X1,X38,X19) )
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),X39))
      <=> hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X38),X39)) ) ),
    c_0_103 ).

fof(c_0_712,axiom,
    ! [X25,X42] :
      ( hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,X25),X42))
    <=> ! [X26] :
          ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X26),arrow_1111136790e_Prof))
         => hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X25,X26) = hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X26,X42) ) ),
    c_0_104 ).

fof(c_0_713,axiom,
    ! [X3] :
      ( ordere223160158up_add(X3)
     => ! [X36,X45,X21,X22] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X22))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X36),X45))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X36)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X22),X45))) ) ) ),
    c_0_105 ).

fof(c_0_714,axiom,
    ! [X3] :
      ( ordere779506340up_add(X3)
     => ! [X36,X45,X21,X22] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X21),X22))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X36),X45))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X36)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X22),X45))) ) ) ),
    c_0_106 ).

fof(c_0_715,axiom,
    ! [X3] :
      ( ordere223160158up_add(X3)
     => ! [X36,X45,X21,X22] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X21),X22))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X36),X45))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X36)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X22),X45))) ) ) ),
    c_0_107 ).

fof(c_0_716,axiom,
    ! [X3] :
      ( ordere223160158up_add(X3)
     => ! [X36,X45,X21,X22] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X22))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X36),X45))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X36)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X22),X45))) ) ) ),
    c_0_108 ).

fof(c_0_717,axiom,
    ! [X42,X63,X37] :
      ( ! [X16,X64] :
          ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X16),X64))
         => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,X37,X16)),hAPP(nat,nat,X37,X64))) )
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X42),X63))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X37,X42)),hAPP(nat,nat,X37,X63))) ) ),
    c_0_109 ).

fof(c_0_718,axiom,
    ! [X52,X61,X58,X59] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X58),X59))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X52),X61))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X58),X52)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X59),X61))) ) ),
    c_0_110 ).

fof(c_0_719,axiom,
    ! [X52,X61,X58,X59] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X58),X59))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X52),X61))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X58),X52)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X59),X61))) ) ),
    c_0_111 ).

fof(c_0_720,plain,
    ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab)),
    inference(fof_simplification,[status(thm)],[c_0_112]) ).

fof(c_0_721,plain,
    ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba)),
    inference(fof_simplification,[status(thm)],[c_0_113]) ).

fof(c_0_722,axiom,
    ! [X1,X3,X39,X37] :
      ( hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X37),top_top(fun(X1,bool))) = top_top(fun(X3,bool))
     => hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X37),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),hAPP(fun(X1,X3),fun(X3,X1),hAPP(fun(X1,bool),fun(fun(X1,X3),fun(X3,X1)),hilbert_inv_into(X1,X3),top_top(fun(X1,bool))),X37)),X39)) = ti(fun(X3,bool),X39) ),
    c_0_114 ).

fof(c_0_723,axiom,
    ! [X3,X1,X7,X37,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X7),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X37),X39)))
     => hAPP(X1,X3,X37,hAPP(X3,X1,hAPP(fun(X1,X3),fun(X3,X1),hAPP(fun(X1,bool),fun(fun(X1,X3),fun(X3,X1)),hilbert_inv_into(X1,X3),X39),X37),X7)) = ti(X3,X7) ),
    c_0_115 ).

fof(c_0_724,axiom,
    ! [X3] :
      ( linordered_idom(X3)
     => ! [X14] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X14),X14)),zero_zero(X3)))
        <=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X14),zero_zero(X3))) ) ),
    c_0_116 ).

fof(c_0_725,axiom,
    ! [X3] :
      ( linord219039673up_add(X3)
     => ! [X14] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X14),X14)),zero_zero(X3)))
        <=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X14),zero_zero(X3))) ) ),
    c_0_117 ).

fof(c_0_726,axiom,
    ! [X3] :
      ( linord219039673up_add(X3)
     => ! [X14] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X14),X14)),zero_zero(X3)))
        <=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X14),zero_zero(X3))) ) ),
    c_0_118 ).

fof(c_0_727,axiom,
    ! [X3] :
      ( ring_1(X3)
     => ! [X15,X14] :
          ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X14),ring_1_Ints(X3)))
         => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X15),ring_1_Ints(X3)))
           => hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X14),X15)),ring_1_Ints(X3))) ) ) ),
    c_0_119 ).

fof(c_0_728,axiom,
    ! [X3,X39,X43] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X43))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43))
       => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X3,bool),nat,finite_card(X3),X39)),hAPP(fun(X3,bool),nat,finite_card(X3),X43)))
         => hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less(fun(X3,bool)),X39),X43)) ) ) ),
    c_0_120 ).

fof(c_0_729,axiom,
    ! [X58,X59,X52] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X58),X59)),X52))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X58),X52)) ),
    c_0_121 ).

fof(c_0_730,axiom,
    ! [X51,X52,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),X52)),X53))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X52),X53)) ),
    c_0_122 ).

fof(c_0_731,axiom,
    ! [X51,X52,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),X52)),X53))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X51),X53)) ),
    c_0_123 ).

fof(c_0_732,plain,
    ! [X51,X52,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),X52)),X53))
     => ~ ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X51),X53))
         => ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X52),X53)) ) ),
    inference(fof_simplification,[status(thm)],[c_0_124]) ).

fof(c_0_733,axiom,
    ! [X3] :
      ( ordere223160158up_add(X3)
     => ! [X36,X21,X22] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X22))
         => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X36)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X22),X36))) ) ),
    c_0_125 ).

fof(c_0_734,axiom,
    ! [X3] :
      ( ordere223160158up_add(X3)
     => ! [X36,X21,X22] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X22))
         => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X36),X21)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X36),X22))) ) ),
    c_0_126 ).

fof(c_0_735,axiom,
    ! [X3] :
      ( ordere779506340up_add(X3)
     => ! [X36,X21,X22] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X21),X22))
         => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X36)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X22),X36))) ) ),
    c_0_127 ).

fof(c_0_736,axiom,
    ! [X3] :
      ( ordere779506340up_add(X3)
     => ! [X36,X21,X22] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X21),X22))
         => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X36),X21)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X36),X22))) ) ),
    c_0_128 ).

fof(c_0_737,axiom,
    ! [X52,X58,X59] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X58),X59))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X58),X52)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X59),X52))) ),
    c_0_129 ).

fof(c_0_738,axiom,
    ! [X52,X58,X59] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X58),X59))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X58),X52)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X59),X52))) ),
    c_0_130 ).

fof(c_0_739,axiom,
    ! [X3,X37,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),hAPP(fun(X3,bool),fun(X3,bool),hAPP(fun(X3,X3),fun(fun(X3,bool),fun(X3,bool)),image(X3,X3),X37),X39)))
       => hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X3),fun(fun(X3,bool),bool),inj_on(X3,X3),X37),X39)) ) ),
    c_0_131 ).

fof(c_0_740,axiom,
    ! [X3] :
      ( ordere216010020id_add(X3)
     => ! [X22,X21] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),zero_zero(X3)))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X22),zero_zero(X3)))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X22)),zero_zero(X3))) ) ) ),
    c_0_132 ).

fof(c_0_741,axiom,
    ! [X3] :
      ( ordere216010020id_add(X3)
     => ! [X22,X21] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X21),zero_zero(X3)))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X22),zero_zero(X3)))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X22)),zero_zero(X3))) ) ) ),
    c_0_133 ).

fof(c_0_742,axiom,
    ! [X3] :
      ( ordere216010020id_add(X3)
     => ! [X22,X21] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),zero_zero(X3)))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X22),zero_zero(X3)))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X22)),zero_zero(X3))) ) ) ),
    c_0_134 ).

fof(c_0_743,axiom,
    ! [X3] :
      ( ordere216010020id_add(X3)
     => ! [X22,X21] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X21),zero_zero(X3)))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X22),zero_zero(X3)))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X22)),zero_zero(X3))) ) ) ),
    c_0_135 ).

fof(c_0_744,axiom,
    ! [X3,X39] : hBOOL(hAPP(fun(fun(X3,X3),bool),bool,hAPP(fun(X3,X3),fun(fun(fun(X3,X3),bool),bool),member(fun(X3,X3)),combi(X3)),hAPP(fun(X3,fun(X3,bool)),fun(fun(X3,X3),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X3,bool)),fun(fun(X3,X3),bool)),pi(X3,X3),X39),hAPP(fun(X3,bool),fun(X3,fun(X3,bool)),combk(fun(X3,bool),X3),X39)))),
    c_0_136 ).

fof(c_0_745,plain,
    ! [X59,X58] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X59),X58)),X58)),
    inference(fof_simplification,[status(thm)],[c_0_137]) ).

fof(c_0_746,plain,
    ! [X58,X59] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X58),X59)),X58)),
    inference(fof_simplification,[status(thm)],[c_0_138]) ).

fof(c_0_747,plain,
    ! [X3,X39] :
      ( ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39))
       => hAPP(fun(X3,bool),nat,finite_card(X3),X39) = hAPP(fun(X3,bool),nat,hAPP(nat,fun(fun(X3,bool),nat),hAPP(fun(X3,nat),fun(nat,fun(fun(X3,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(X3,nat),fun(nat,fun(fun(X3,bool),nat))),finite_fold_image(nat,X3),plus_plus(nat)),hAPP(nat,fun(X3,nat),combk(nat,X3),one_one(nat))),zero_zero(nat)),X39) )
      & ( ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39))
       => hAPP(fun(X3,bool),nat,finite_card(X3),X39) = zero_zero(nat) ) ),
    inference(fof_simplification,[status(thm)],[c_0_139]) ).

fof(c_0_748,axiom,
    ! [X3,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39))
     => hAPP(fun(X3,bool),nat,finite_card(X3),X39) = hAPP(fun(X3,bool),nat,hAPP(nat,fun(fun(X3,bool),nat),hAPP(fun(X3,nat),fun(nat,fun(fun(X3,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(X3,nat),fun(nat,fun(fun(X3,bool),nat))),finite_fold_image(nat,X3),plus_plus(nat)),hAPP(nat,fun(X3,nat),combk(nat,X3),one_one(nat))),zero_zero(nat)),X39) ),
    c_0_140 ).

fof(c_0_749,axiom,
    ! [X3,X39,X43] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X43))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43))
       => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X3,bool),nat,finite_card(X3),X43)),hAPP(fun(X3,bool),nat,finite_card(X3),X39)))
         => ti(fun(X3,bool),X39) = ti(fun(X3,bool),X43) ) ) ),
    c_0_141 ).

fof(c_0_750,axiom,
    ! [X57,X60] : hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,nat),fun(fun(nat,bool),bool),inj_on(nat,nat),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),X57)),X60)),
    c_0_142 ).

fof(c_0_751,axiom,
    ! [X57] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),X57)))),
    c_0_143 ).

fof(c_0_752,axiom,
    ! [X57] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X57)))),
    c_0_144 ).

fof(c_0_753,axiom,
    ! [X3] :
      ( comm_semiring_1(X3)
     => ! [X21,X22,X36,X45] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X22)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X36),X45)) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X36)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X22),X45)) ),
    c_0_145 ).

fof(c_0_754,axiom,
    ! [X1,X3,X37,X6,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X39))
     => hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X3,X1,X37,X6)),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X37),X39))) ),
    c_0_146 ).

fof(c_0_755,axiom,
    ! [X54,X29] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),X29)))
    <=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X54))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X29)) ) ),
    c_0_147 ).

fof(c_0_756,axiom,
    ! [X3,X1,X39,X43] :
      ( hBOOL(hAPP(fun(sum_sum(X3,X1),bool),bool,finite_finite_1(sum_sum(X3,X1)),hAPP(fun(X1,bool),fun(sum_sum(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X1,bool),fun(sum_sum(X3,X1),bool)),sum_Plus(X3,X1),X39),X43)))
     => hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43)) ),
    c_0_148 ).

fof(c_0_757,axiom,
    ! [X3,X1,X39,X43] :
      ( hBOOL(hAPP(fun(sum_sum(X3,X1),bool),bool,finite_finite_1(sum_sum(X3,X1)),hAPP(fun(X1,bool),fun(sum_sum(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X1,bool),fun(sum_sum(X3,X1),bool)),sum_Plus(X3,X1),X39),X43)))
     => hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39)) ),
    c_0_149 ).

fof(c_0_758,axiom,
    ! [X3,X1,X39,X43] :
      ( hBOOL(hAPP(fun(sum_sum(X3,X1),bool),bool,finite_finite_1(sum_sum(X3,X1)),hAPP(fun(X1,bool),fun(sum_sum(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X1,bool),fun(sum_sum(X3,X1),bool)),sum_Plus(X3,X1),X39),X43)))
    <=> ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39))
        & hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43)) ) ),
    c_0_150 ).

fof(c_0_759,axiom,
    ! [X1,X3,X50,X11] :
      ( ! [X26,X46] :
          ( hBOOL(hAPP(X1,bool,hAPP(X3,fun(X1,bool),X11,X26),X46))
         => hBOOL(hAPP(X1,bool,hAPP(X3,fun(X1,bool),X50,X26),X46)) )
     => hBOOL(hAPP(fun(X3,fun(X1,bool)),bool,hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,fun(X1,bool)),bool),ord_less_eq(fun(X3,fun(X1,bool))),X11),X50)) ),
    c_0_151 ).

fof(c_0_760,axiom,
    ! [X3] :
      ( ordere216010020id_add(X3)
     => ! [X22,X21] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),X21))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X22))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X22))) ) ) ),
    c_0_152 ).

fof(c_0_761,axiom,
    ! [X3] :
      ( ordere216010020id_add(X3)
     => ! [X22,X21] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X21))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),X22))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X22))) ) ) ),
    c_0_153 ).

fof(c_0_762,axiom,
    ! [X3] :
      ( ordere216010020id_add(X3)
     => ! [X22,X21] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),X21))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),X22))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X22))) ) ) ),
    c_0_154 ).

fof(c_0_763,axiom,
    ! [X3] :
      ( ordere216010020id_add(X3)
     => ! [X22,X21] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X21))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X22))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X22))) ) ) ),
    c_0_155 ).

fof(c_0_764,axiom,
    ! [X1,X3,X2,X37,X38] : hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),hAPP(fun(X1,X2),fun(X1,X3),hAPP(fun(X2,X3),fun(fun(X1,X2),fun(X1,X3)),combb(X2,X3,X1),X37),X38)),top_top(fun(X1,bool))) = hAPP(fun(X2,bool),fun(X3,bool),hAPP(fun(X2,X3),fun(fun(X2,bool),fun(X3,bool)),image(X2,X3),X37),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X38),top_top(fun(X1,bool)))),
    c_0_156 ).

fof(c_0_765,axiom,
    ! [X14,X15] :
      ( ti(arrow_490897120le_alt,X14) != ti(arrow_490897120le_alt,X15)
     => ? [X26] :
          ( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X26),arrow_2064824852le_Lin))
          & hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X14),X15)),X26)) ) ),
    c_0_157 ).

fof(c_0_766,axiom,
    ! [X3] :
      ( ordere216010020id_add(X3)
     => ! [X22,X36,X21] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),X21))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X22),X36))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X22),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X36))) ) ) ),
    c_0_158 ).

fof(c_0_767,axiom,
    ! [X3] :
      ( ordere216010020id_add(X3)
     => ! [X22,X36,X21] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X21))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X22),X36))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X22),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X36))) ) ) ),
    c_0_159 ).

fof(c_0_768,axiom,
    ! [X3] :
      ( linordered_semidom(X3)
     => ! [X22,X36,X21] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),X21))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X22),X36))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X22),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X36))) ) ) ),
    c_0_160 ).

fof(c_0_769,axiom,
    ! [X3] :
      ( ordere216010020id_add(X3)
     => ! [X22,X36,X21] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X21))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X22),X36))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X22),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X36))) ) ) ),
    c_0_161 ).

fof(c_0_770,axiom,
    ! [X3] :
      ( ordere216010020id_add(X3)
     => ! [X22,X21,X36] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X36))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X22),X21))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X22),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X36))) ) ) ),
    c_0_162 ).

fof(c_0_771,axiom,
    ! [X3] :
      ( linordered_field(X3)
     => ! [X33,X34] :
          ( ! [X75] :
              ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),X75))
             => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X33),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X34),X75))) )
         => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X33),X34)) ) ),
    c_0_163 ).

fof(c_0_772,plain,
    ~ ! [X31] :
        ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),X31))
       => ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X31),arrow_2064824852le_Lin)) ),
    inference(fof_simplification,[status(thm)],[c_0_164]) ).

fof(c_0_773,plain,
    ~ ! [X30] :
        ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),X30))
       => ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X30),arrow_2064824852le_Lin)) ),
    inference(fof_simplification,[status(thm)],[c_0_165]) ).

fof(c_0_774,axiom,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba)),
    c_0_166 ).

fof(c_0_775,axiom,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab)),
    c_0_167 ).

fof(c_0_776,axiom,
    ! [X1,X3,X2,X37,X38,X39] : hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X37),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X38),X39)) = hAPP(fun(X2,bool),fun(X3,bool),hAPP(fun(X2,X3),fun(fun(X2,bool),fun(X3,bool)),image(X2,X3),hAPP(fun(X2,X1),fun(X2,X3),hAPP(fun(X1,X3),fun(fun(X2,X1),fun(X2,X3)),combb(X1,X3,X2),X37),X38)),X39),
    c_0_168 ).

fof(c_0_777,axiom,
    ! [X3] :
      ( dense_linorder(X3)
     => ! [X35,X33,X34] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X34))
         => ( ! [X47] :
                ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X47))
               => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X47),X34))
                 => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X47),X35)) ) )
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X34),X35)) ) ) ),
    c_0_169 ).

fof(c_0_778,axiom,
    ! [X3,X1,X6,X7,X37,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),X39))
     => ( hAPP(X3,X1,X37,X6) = hAPP(X3,X1,X37,X7)
       => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X39))
         => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X7),X39))
           => ti(X3,X6) = ti(X3,X7) ) ) ) ),
    c_0_170 ).

fof(c_0_779,axiom,
    ! [X3,X1,X7,X6,X37,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),X39))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X39))
       => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X7),X39))
         => ( hAPP(X3,X1,X37,X6) = hAPP(X3,X1,X37,X7)
          <=> ti(X3,X6) = ti(X3,X7) ) ) ) ),
    c_0_171 ).

fof(c_0_780,axiom,
    ! [X3,X1,X6,X7,X37,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),X39))
     => ( ti(X3,X6) != ti(X3,X7)
       => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X39))
         => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X7),X39))
           => hAPP(X3,X1,X37,X6) != hAPP(X3,X1,X37,X7) ) ) ) ),
    c_0_172 ).

fof(c_0_781,axiom,
    ! [X3,X1,X37,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),X39))
    <=> ! [X26] :
          ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X26),X39))
         => ! [X27] :
              ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X27),X39))
             => ( hAPP(X3,X1,X37,X26) = hAPP(X3,X1,X37,X27)
               => ti(X3,X26) = ti(X3,X27) ) ) ) ),
    c_0_173 ).

fof(c_0_782,axiom,
    ! [X1,X3,X15,X37,X6,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X39))
     => ( ti(X1,X15) = hAPP(X3,X1,X37,X6)
       => hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X15),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X37),X39))) ) ),
    c_0_174 ).

fof(c_0_783,axiom,
    ! [X3,X1,X39,X15,X37,X6] :
      ( ti(X3,X15) = hAPP(X1,X3,X37,X6)
     => ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X39))
       => hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X15),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X37),X39))) ) ),
    c_0_175 ).

fof(c_0_784,axiom,
    ! [X3,X1,X11] :
      ( ! [X18] : hBOOL(hAPP(product_prod(X3,X1),bool,X11,X18))
    <=> ! [X19,X20] : hBOOL(hAPP(product_prod(X3,X1),bool,X11,hAPP(X1,product_prod(X3,X1),hAPP(X3,fun(X1,product_prod(X3,X1)),product_Pair(X3,X1),X19),X20))) ),
    c_0_176 ).

fof(c_0_785,axiom,
    ! [X3] :
      ( linord219039673up_add(X3)
     => ! [X14] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X14),X14)))
        <=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),X14)) ) ),
    c_0_177 ).

fof(c_0_786,axiom,
    ! [X3] :
      ( linord219039673up_add(X3)
     => ! [X14] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X14),X14)))
        <=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X14)) ) ),
    c_0_178 ).

fof(c_0_787,axiom,
    ! [X3,X1,X6,X37,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),X39))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X39))
       => hAPP(X1,X3,hAPP(fun(X3,X1),fun(X1,X3),hAPP(fun(X3,bool),fun(fun(X3,X1),fun(X1,X3)),hilbert_inv_into(X3,X1),X39),X37),hAPP(X3,X1,X37,X6)) = ti(X3,X6) ) ),
    c_0_179 ).

fof(c_0_788,axiom,
    ! [X3,X1,X6,X7,X11,X50] :
      ( hBOOL(hAPP(fun(X3,fun(X1,bool)),bool,hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,fun(X1,bool)),bool),ord_less_eq(fun(X3,fun(X1,bool))),X11),X50))
     => ( hBOOL(hAPP(X1,bool,hAPP(X3,fun(X1,bool),X11,X6),X7))
       => hBOOL(hAPP(X1,bool,hAPP(X3,fun(X1,bool),X50,X6),X7)) ) ),
    c_0_180 ).

fof(c_0_789,axiom,
    ! [X1,X3,X50,X11,X6,X7] :
      ( hBOOL(hAPP(X1,bool,hAPP(X3,fun(X1,bool),X11,X6),X7))
     => ( hBOOL(hAPP(fun(X3,fun(X1,bool)),bool,hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,fun(X1,bool)),bool),ord_less_eq(fun(X3,fun(X1,bool))),X11),X50))
       => hBOOL(hAPP(X1,bool,hAPP(X3,fun(X1,bool),X50,X6),X7)) ) ),
    c_0_181 ).

fof(c_0_790,axiom,
    ! [X3,X39,X43] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X43))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X3,bool),nat,finite_card(X3),X39)),hAPP(fun(X3,bool),nat,finite_card(X3),X43))) ) ),
    c_0_182 ).

fof(c_0_791,axiom,
    ! [X3,X39,X43] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X43))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less(fun(X3,bool)),X39),X43))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X3,bool),nat,finite_card(X3),X39)),hAPP(fun(X3,bool),nat,finite_card(X3),X43))) ) ),
    c_0_183 ).

fof(c_0_792,axiom,
    ! [X3,X1,X7,X6,X37,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),X39))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X39))
       => ( hAPP(X3,X1,X37,X6) = ti(X1,X7)
         => hAPP(X1,X3,hAPP(fun(X3,X1),fun(X1,X3),hAPP(fun(X3,bool),fun(fun(X3,X1),fun(X1,X3)),hilbert_inv_into(X3,X1),X39),X37),X7) = ti(X3,X6) ) ) ),
    c_0_184 ).

fof(c_0_793,axiom,
    ! [X11,X54,X29] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X29))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X11,X29),X54)) )
     => ( ( X54 = X29
         => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X11,X29),X54)) )
       => ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X29),X54))
           => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X11,X29),X54)) )
         => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X11,X29),X54)) ) ) ),
    c_0_185 ).

fof(c_0_794,axiom,
    ! [X58,X51] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X58),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X58),X51)))),
    c_0_186 ).

fof(c_0_795,axiom,
    ! [X58,X51] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X58),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),X58)))),
    c_0_187 ).

fof(c_0_796,axiom,
    ! [X3,X49,X39,X43] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less(fun(X3,bool)),X39),X43))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less(fun(X3,bool)),X43),X49))
       => hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less(fun(X3,bool)),X39),X49)) ) ),
    c_0_188 ).

fof(c_0_797,axiom,
    ! [X3,X49,X39,X43] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X43),X49))
       => hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X49)) ) ),
    c_0_189 ).

fof(c_0_798,axiom,
    ! [X3,X49,X39,X43] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less(fun(X3,bool)),X43),X49))
       => hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less(fun(X3,bool)),X39),X49)) ) ),
    c_0_190 ).

fof(c_0_799,axiom,
    ! [X3,X49,X39,X43] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less(fun(X3,bool)),X39),X43))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X43),X49))
       => hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less(fun(X3,bool)),X39),X49)) ) ),
    c_0_191 ).

fof(c_0_800,axiom,
    ! [X51,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X51)),hAPP(nat,nat,suc,X53)))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),X53)) ),
    c_0_192 ).

fof(c_0_801,axiom,
    ! [X54,X29] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X54)),hAPP(nat,nat,suc,X29)))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X29)) ),
    c_0_193 ).

fof(c_0_802,axiom,
    ! [X29,X54] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X29)),hAPP(nat,nat,suc,X54)))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X29),X54)) ),
    c_0_194 ).

fof(c_0_803,axiom,
    ! [X3,X1,X37,X6] : hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),hAPP(X1,X3,X37,X6)),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X37),top_top(fun(X1,bool))))),
    c_0_195 ).

fof(c_0_804,axiom,
    ! [X3,X1,X39,X37,X43] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),X43))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43))
       => hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),X39)) ) ),
    c_0_196 ).

fof(c_0_805,axiom,
    ! [X52,X58,X59] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X58),X59))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X59),X52))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X58)),X52)) ) ),
    c_0_197 ).

fof(c_0_806,axiom,
    ! [X3,X1,X38,X37] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),top_top(fun(X3,bool))))
     => ( ! [X26] : hAPP(X3,X1,X37,hAPP(X1,X3,X38,X26)) = ti(X1,X26)
       => hAPP(fun(X3,X1),fun(X1,X3),hAPP(fun(X3,bool),fun(fun(X3,X1),fun(X1,X3)),hilbert_inv_into(X3,X1),top_top(fun(X3,bool))),X37) = ti(fun(X1,X3),X38) ) ),
    c_0_198 ).

fof(c_0_807,axiom,
    ! [X3] :
      ( comm_semiring_1(X3)
     => ! [X21,X22,X36] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X22)),X36) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X36)),X22) ),
    c_0_199 ).

fof(c_0_808,axiom,
    ! [X1,X3,X43,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39))
     => ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43))
       => hBOOL(hAPP(fun(sum_sum(X3,X1),bool),bool,finite_finite_1(sum_sum(X3,X1)),hAPP(fun(X1,bool),fun(sum_sum(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X1,bool),fun(sum_sum(X3,X1),bool)),sum_Plus(X3,X1),X39),X43))) ) ),
    c_0_200 ).

fof(c_0_809,axiom,
    ! [X3,X17,X39,X43] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less(fun(X3,bool)),X39),X43))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X17),X39))
       => hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X17),X43)) ) ),
    c_0_201 ).

fof(c_0_810,axiom,
    ! [X3,X6,X39,X43] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X39))
       => hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X43)) ) ),
    c_0_202 ).

fof(c_0_811,axiom,
    ! [X3,X43,X6,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X39))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43))
       => hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X43)) ) ),
    c_0_203 ).

fof(c_0_812,axiom,
    ! [X3,X6,X39,X43] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X39))
       => hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X43)) ) ),
    c_0_204 ).

fof(c_0_813,axiom,
    ! [X3,X17,X39,X43] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X17),X39))
       => hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X17),X43)) ) ),
    c_0_205 ).

fof(c_0_814,axiom,
    ! [X3,X1] :
      ( ord(X1)
     => ! [X6,X37,X38] :
          ( hBOOL(hAPP(fun(X3,X1),bool,hAPP(fun(X3,X1),fun(fun(X3,X1),bool),ord_less_eq(fun(X3,X1)),X37),X38))
         => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X3,X1,X37,X6)),hAPP(X3,X1,X38,X6))) ) ),
    c_0_206 ).

fof(c_0_815,axiom,
    ! [X3,X1] :
      ( ord(X1)
     => ! [X6,X37,X38] :
          ( hBOOL(hAPP(fun(X3,X1),bool,hAPP(fun(X3,X1),fun(fun(X3,X1),bool),ord_less_eq(fun(X3,X1)),X37),X38))
         => hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X3,X1,X37,X6)),hAPP(X3,X1,X38,X6))) ) ),
    c_0_207 ).

fof(c_0_816,plain,
    ! [X54,X29] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X29))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X29)),X54)) ),
    inference(fof_simplification,[status(thm)],[c_0_208]) ).

fof(c_0_817,axiom,
    ! [X3] :
      ( linorder(X3)
     => ! [X14,X15,X17,X79] :
          ( hAPP(X3,fun(X3,bool),hAPP(X3,fun(X3,fun(X3,bool)),ord_atLeastLessThan(X3),X14),X15) = hAPP(X3,fun(X3,bool),hAPP(X3,fun(X3,fun(X3,bool)),ord_atLeastLessThan(X3),X17),X79)
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X14),X15))
           => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X17),X79))
             => ti(X3,X15) = ti(X3,X79) ) ) ) ),
    c_0_209 ).

fof(c_0_818,axiom,
    ! [X3] :
      ( linorder(X3)
     => ! [X14,X15,X17,X79] :
          ( hAPP(X3,fun(X3,bool),hAPP(X3,fun(X3,fun(X3,bool)),ord_atLeastLessThan(X3),X14),X15) = hAPP(X3,fun(X3,bool),hAPP(X3,fun(X3,fun(X3,bool)),ord_atLeastLessThan(X3),X17),X79)
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X14),X15))
           => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X17),X79))
             => ti(X3,X14) = ti(X3,X17) ) ) ) ),
    c_0_210 ).

fof(c_0_819,axiom,
    ! [X3] :
      ( linorder(X3)
     => ! [X17,X79,X14,X15] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X14),X15))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X17),X79))
           => ( hAPP(X3,fun(X3,bool),hAPP(X3,fun(X3,fun(X3,bool)),ord_atLeastLessThan(X3),X14),X15) = hAPP(X3,fun(X3,bool),hAPP(X3,fun(X3,fun(X3,bool)),ord_atLeastLessThan(X3),X17),X79)
            <=> ( ti(X3,X14) = ti(X3,X17)
                & ti(X3,X15) = ti(X3,X79) ) ) ) ) ),
    c_0_211 ).

fof(c_0_820,plain,
    ! [X3,X1] :
      ( ord(X1)
     => ! [X37,X38] :
          ( hBOOL(hAPP(fun(X3,X1),bool,hAPP(fun(X3,X1),fun(fun(X3,X1),bool),ord_less(fun(X3,X1)),X37),X38))
        <=> ( hBOOL(hAPP(fun(X3,X1),bool,hAPP(fun(X3,X1),fun(fun(X3,X1),bool),ord_less_eq(fun(X3,X1)),X37),X38))
            & ~ hBOOL(hAPP(fun(X3,X1),bool,hAPP(fun(X3,X1),fun(fun(X3,X1),bool),ord_less_eq(fun(X3,X1)),X38),X37)) ) ) ),
    inference(fof_simplification,[status(thm)],[c_0_212]) ).

fof(c_0_821,axiom,
    ! [X1,X3,X43,X39] :
      ( ( ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39))
          & hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43)) )
       => hAPP(fun(sum_sum(X3,X1),bool),nat,finite_card(sum_sum(X3,X1)),hAPP(fun(X1,bool),fun(sum_sum(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X1,bool),fun(sum_sum(X3,X1),bool)),sum_Plus(X3,X1),X39),X43)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X3,bool),nat,finite_card(X3),X39)),hAPP(fun(X1,bool),nat,finite_card(X1),X43)) )
      & ( ~ ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39))
            & hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43)) )
       => hAPP(fun(sum_sum(X3,X1),bool),nat,finite_card(sum_sum(X3,X1)),hAPP(fun(X1,bool),fun(sum_sum(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X1,bool),fun(sum_sum(X3,X1),bool)),sum_Plus(X3,X1),X39),X43)) = zero_zero(nat) ) ),
    c_0_213 ).

fof(c_0_822,axiom,
    ! [X1,X3,X43,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39))
     => ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X43))
       => hAPP(fun(sum_sum(X3,X1),bool),nat,finite_card(sum_sum(X3,X1)),hAPP(fun(X1,bool),fun(sum_sum(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X1,bool),fun(sum_sum(X3,X1),bool)),sum_Plus(X3,X1),X39),X43)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X3,bool),nat,finite_card(X3),X39)),hAPP(fun(X1,bool),nat,finite_card(X1),X43)) ) ),
    c_0_214 ).

fof(c_0_823,axiom,
    ! [X1,X3,X37,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),X39))
      <=> hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X37),X39)) = hAPP(fun(X3,bool),nat,finite_card(X3),X39) ) ),
    c_0_215 ).

fof(c_0_824,axiom,
    ! [X1,X3,X37,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39))
     => ( hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X37),X39)) = hAPP(fun(X3,bool),nat,finite_card(X3),X39)
       => hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),X39)) ) ),
    c_0_216 ).

fof(c_0_825,axiom,
    ! [X35,X33,X34] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X33),X34))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X33),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X34),X35))) ),
    c_0_217 ).

fof(c_0_826,axiom,
    ! [X34,X33,X35] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X33),X35))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X33),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X34),X35))) ),
    c_0_218 ).

fof(c_0_827,axiom,
    ! [X34,X33,X35] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X33),X35))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X33),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X34),X35))) ),
    c_0_219 ).

fof(c_0_828,axiom,
    ! [X35,X33,X34] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X33),X34))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X33),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X34),X35))) ),
    c_0_220 ).

fof(c_0_829,axiom,
    ! [X51,X58,X59] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X58),X59))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X58),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),X59))) ),
    c_0_221 ).

fof(c_0_830,axiom,
    ! [X51,X58,X59] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X58),X59))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X58),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X59),X51))) ),
    c_0_222 ).

fof(c_0_831,axiom,
    ! [X51,X58,X59] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X58),X59))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X58),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),X59))) ),
    c_0_223 ).

fof(c_0_832,axiom,
    ! [X51,X58,X59] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X58),X59))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X58),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X59),X51))) ),
    c_0_224 ).

fof(c_0_833,axiom,
    ! [X58,X52] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X58)),X52))
     => ~ ! [X64] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X58),X64))
           => X52 != hAPP(nat,nat,suc,X64) ) ),
    c_0_225 ).

fof(c_0_834,axiom,
    ! [X29,X54] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X29),X54))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X29)),X54)) ),
    c_0_226 ).

fof(c_0_835,axiom,
    ! [X54,X29] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X54)),X29))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X29)) ),
    c_0_227 ).

fof(c_0_836,axiom,
    ! [X51,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X51)),X53))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),X53)) ),
    c_0_228 ).

fof(c_0_837,axiom,
    ! [X51,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X51)),X53))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),X53)) ),
    c_0_229 ).

fof(c_0_838,axiom,
    ! [X51,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X51)),X53))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X51),X53)) ),
    c_0_230 ).

fof(c_0_839,axiom,
    ! [X3,X1,X15,X37,X6] :
      ( ti(X3,X15) = hAPP(X1,X3,X37,X6)
     => hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X15),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X37),top_top(fun(X1,bool))))) ),
    c_0_231 ).

fof(c_0_840,axiom,
    ! [X51,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),X53))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X51)),hAPP(nat,nat,suc,X53))) ),
    c_0_232 ).

fof(c_0_841,axiom,
    ! [X3,X39,X43] :
      ( ti(fun(X3,bool),X39) = ti(fun(X3,bool),X43)
    <=> ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43))
        & hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X43),X39)) ) ),
    c_0_233 ).

fof(c_0_842,axiom,
    ! [X3,X39,X43] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X43),X39))
       => ti(fun(X3,bool),X39) = ti(fun(X3,bool),X43) ) ),
    c_0_234 ).

fof(c_0_843,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X35,X34,X33] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X34),X33))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X35),X34))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X35),X33)) ) ) ),
    c_0_235 ).

fof(c_0_844,axiom,
    ! [X3] :
      ( preorder(X3)
     => ! [X35,X33,X34] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X33),X34))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X34),X35))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X35)) ) ) ),
    c_0_236 ).

fof(c_0_845,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X35,X34,X33] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X34),X33))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X35),X34))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X35),X33)) ) ) ),
    c_0_237 ).

fof(c_0_846,axiom,
    ! [X3] :
      ( preorder(X3)
     => ! [X35,X33,X34] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X34))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X34),X35))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X35)) ) ) ),
    c_0_238 ).

fof(c_0_847,axiom,
    ! [X3] :
      ( preorder(X3)
     => ! [X35,X33,X34] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X33),X34))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X34),X35))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X33),X35)) ) ) ),
    c_0_239 ).

fof(c_0_848,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X35,X34,X33] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X34),X33))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X35),X34))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X35),X33)) ) ) ),
    c_0_240 ).

fof(c_0_849,axiom,
    ! [X3] :
      ( preorder(X3)
     => ! [X35,X33,X34] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X34))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X34),X35))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X35)) ) ) ),
    c_0_241 ).

fof(c_0_850,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X35,X34,X33] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X34),X33))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X35),X34))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X35),X33)) ) ) ),
    c_0_242 ).

fof(c_0_851,axiom,
    ! [X3,X1,X6,X37] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),top_top(fun(X3,bool))))
     => hAPP(X1,X3,hAPP(fun(X3,X1),fun(X1,X3),hAPP(fun(X3,bool),fun(fun(X3,X1),fun(X1,X3)),hilbert_inv_into(X3,X1),top_top(fun(X3,bool))),X37),hAPP(X3,X1,X37,X6)) = ti(X3,X6) ),
    c_0_243 ).

fof(c_0_852,axiom,
    hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),p),arrow_1111136790e_Prof)),
    c_0_244 ).

fof(c_0_853,axiom,
    ! [X3,X1,X6,X7,X37] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),top_top(fun(X3,bool))))
     => ( hAPP(X3,X1,X37,X6) = ti(X1,X7)
       => hAPP(X1,X3,hAPP(fun(X3,X1),fun(X1,X3),hAPP(fun(X3,bool),fun(fun(X3,X1),fun(X1,X3)),hilbert_inv_into(X3,X1),top_top(fun(X3,bool))),X37),X7) = ti(X3,X6) ) ),
    c_0_245 ).

fof(c_0_854,axiom,
    ! [X52,X58,X59] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X58),X59))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X59),X52))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X58),X52)) ) ),
    c_0_246 ).

fof(c_0_855,axiom,
    arrow_1111136790e_Prof = hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(arrow_660593299e_indi,bool),fun(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),top_top(fun(arrow_660593299e_indi,bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),arrow_660593299e_indi),arrow_2064824852le_Lin)),
    c_0_247 ).

fof(c_0_856,axiom,
    ! [X51,X53,X52,X61] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X52),X61))
     => ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),X61) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X52),X53)
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),X53)) ) ),
    c_0_248 ).

fof(c_0_857,axiom,
    ! [X3] :
      ( comm_semiring_1(X3)
     => ! [X21,X22,X36] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X22)),X36) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X22),X36)) ),
    c_0_249 ).

fof(c_0_858,axiom,
    ! [X3] :
      ( comm_semiring_1(X3)
     => ! [X21,X36,X45] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X36),X45)) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X36)),X45) ),
    c_0_250 ).

fof(c_0_859,axiom,
    ! [X3] :
      ( ab_semigroup_add(X3)
     => ! [X21,X22,X36] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X22)),X36) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X22),X36)) ),
    c_0_251 ).

fof(c_0_860,axiom,
    ! [X54,X29] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X29))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X29),hAPP(nat,nat,suc,X54)))
      <=> X29 = X54 ) ),
    c_0_252 ).

fof(c_0_861,plain,
    ! [X54,X29] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X29))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X29),hAPP(nat,nat,suc,X54))) ),
    inference(fof_simplification,[status(thm)],[c_0_253]) ).

fof(c_0_862,axiom,
    ! [X3] :
      ( ordere216010020id_add(X3)
     => ! [X7,X6] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X6))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),X7))
           => ( hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X6),X7) = zero_zero(X3)
            <=> ( ti(X3,X6) = zero_zero(X3)
                & ti(X3,X7) = zero_zero(X3) ) ) ) ) ),
    c_0_254 ).

fof(c_0_863,axiom,
    ! [X51,X53,X52] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),X53)),X52) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X53),X52)),
    c_0_255 ).

fof(c_0_864,axiom,
    ! [X51,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),X53))
     => ( hAPP(nat,nat,suc,X51) != X53
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X51)),X53)) ) ),
    c_0_256 ).

fof(c_0_865,axiom,
    ! [X51,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),X53))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X51)),X53)) ),
    c_0_257 ).

fof(c_0_866,axiom,
    ! [X29] : hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),X29))) = hAPP(nat,nat,suc,X29),
    c_0_258 ).

fof(c_0_867,axiom,
    ! [X1,X3,X76,X25] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X25))
     => hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X76),X25))) ),
    c_0_259 ).

fof(c_0_868,axiom,
    ! [X1,X3,X37,X39] :
      ( ! [X26,X46] :
          ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X26),X39))
         => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X46),X39))
           => ( hAPP(X3,X1,X37,X26) = hAPP(X3,X1,X37,X46)
             => ti(X3,X26) = ti(X3,X46) ) ) )
     => hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),X39)) ),
    c_0_260 ).

fof(c_0_869,plain,
    ! [X51,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X51),hAPP(nat,nat,suc,X53)))
     => ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X51),X53))
       => X51 = hAPP(nat,nat,suc,X53) ) ),
    inference(fof_simplification,[status(thm)],[c_0_261]) ).

fof(c_0_870,axiom,
    ! [X54,X29] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),hAPP(nat,nat,suc,X29)))
    <=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X29))
        | X54 = hAPP(nat,nat,suc,X29) ) ),
    c_0_262 ).

fof(c_0_871,axiom,
    ! [X53,X73] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X53)),X73))
     => ? [X32] : X73 = hAPP(nat,nat,suc,X32) ),
    c_0_263 ).

fof(c_0_872,axiom,
    ! [X11,X42,X63] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X42),X63))
     => ( hBOOL(hAPP(nat,bool,X11,X63))
       => ( ! [X16] :
              ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X16),X63))
             => ( hBOOL(hAPP(nat,bool,X11,hAPP(nat,nat,suc,X16)))
               => hBOOL(hAPP(nat,bool,X11,X16)) ) )
         => hBOOL(hAPP(nat,bool,X11,X42)) ) ) ),
    c_0_264 ).

fof(c_0_873,plain,
    ! [X3] :
      ( preorder(X3)
     => ! [X6,X7] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X6),X7))
        <=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X6),X7))
            & ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X7),X6)) ) ) ),
    inference(fof_simplification,[status(thm)],[c_0_265]) ).

fof(c_0_874,axiom,
    ! [X29] : hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X29))) = X29,
    c_0_266 ).

fof(c_0_875,axiom,
    ! [X54,X29] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),hAPP(nat,nat,suc,X29)))
    <=> ( X54 = zero_zero(nat)
        | ? [X64] :
            ( X54 = hAPP(nat,nat,suc,X64)
            & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X64),X29)) ) ) ),
    c_0_267 ).

fof(c_0_876,axiom,
    ! [X3,X43,X39] :
      ( ! [X26] :
          ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X26),X39))
         => hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X26),X43)) )
     => hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43)) ),
    c_0_268 ).

fof(c_0_877,axiom,
    ! [X3,X37] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),top_top(fun(X3,bool))))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X3),fun(fun(X3,bool),bool),inj_on(X3,X3),X37),top_top(fun(X3,bool))))
       => hAPP(fun(X3,bool),fun(X3,bool),hAPP(fun(X3,X3),fun(fun(X3,bool),fun(X3,bool)),image(X3,X3),X37),top_top(fun(X3,bool))) = top_top(fun(X3,bool)) ) ),
    c_0_269 ).

fof(c_0_878,plain,
    ! [X51,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),hAPP(nat,nat,suc,X53)))
     => ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),X53))
       => X51 = X53 ) ),
    inference(fof_simplification,[status(thm)],[c_0_270]) ).

fof(c_0_879,plain,
    ! [X53,X51] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X53),X51))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X53),hAPP(nat,nat,suc,X51)))
       => X51 = X53 ) ),
    inference(fof_simplification,[status(thm)],[c_0_271]) ).

fof(c_0_880,plain,
    ! [X29,X54] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X29),X54))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X29),hAPP(nat,nat,suc,X54)))
      <=> X29 = X54 ) ),
    inference(fof_simplification,[status(thm)],[c_0_272]) ).

fof(c_0_881,axiom,
    ! [X54,X29] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),hAPP(nat,nat,suc,X29)))
    <=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X29))
        | X54 = X29 ) ),
    c_0_273 ).

fof(c_0_882,axiom,
    ! [X54,X29] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),hAPP(nat,nat,suc,X29)))
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X29)) ),
    c_0_274 ).

fof(c_0_883,plain,
    ! [X53] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X53)),X53)),
    inference(fof_simplification,[status(thm)],[c_0_275]) ).

fof(c_0_884,axiom,
    ! [X3,X39,X43] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43))
    <=> ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less(fun(X3,bool)),X39),X43))
        | ti(fun(X3,bool),X39) = ti(fun(X3,bool),X43) ) ),
    c_0_276 ).

fof(c_0_885,axiom,
    ! [X3,X39,X43] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less(fun(X3,bool)),X39),X43))
    <=> ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43))
        & ti(fun(X3,bool),X39) != ti(fun(X3,bool),X43) ) ),
    c_0_277 ).

fof(c_0_886,axiom,
    ! [X3,X39,X43] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less(fun(X3,bool)),X39),X43))
     => hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43)) ),
    c_0_278 ).

fof(c_0_887,axiom,
    ! [X60] :
      ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X60))
    <=> ? [X32] :
        ! [X26] :
          ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X26),X60))
         => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X26),X32)) ) ),
    c_0_279 ).

fof(c_0_888,axiom,
    ! [X60] :
      ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X60))
    <=> ? [X32] :
        ! [X26] :
          ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X26),X60))
         => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X26),X32)) ) ),
    c_0_280 ).

fof(c_0_889,plain,
    ! [X29,X11] :
      ( ~ hBOOL(hAPP(nat,bool,X11,zero_zero(nat)))
     => ( hBOOL(hAPP(nat,bool,X11,X29))
       => ? [X62] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X62),X29))
            & ! [X16] :
                ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X16),X62))
               => ~ hBOOL(hAPP(nat,bool,X11,X16)) )
            & hBOOL(hAPP(nat,bool,X11,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X62),one_one(nat)))) ) ) ),
    inference(fof_simplification,[status(thm)],[c_0_281]) ).

fof(c_0_890,plain,
    ! [X3] :
      ( linorder(X3)
     => ! [X6,X7] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X6),X7))
         => ( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X6),X7))
          <=> ti(X3,X6) = ti(X3,X7) ) ) ),
    inference(fof_simplification,[status(thm)],[c_0_282]) ).

fof(c_0_891,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X6,X7] :
          ( ti(X3,X6) = ti(X3,X7)
        <=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X6),X7))
            & hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X7),X6)) ) ) ),
    c_0_283 ).

fof(c_0_892,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X7,X6] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X7),X6))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X6),X7))
          <=> ti(X3,X6) = ti(X3,X7) ) ) ),
    c_0_284 ).

fof(c_0_893,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X33,X34] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X33),X34))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X34),X33))
           => ti(X3,X33) = ti(X3,X34) ) ) ),
    c_0_285 ).

fof(c_0_894,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X34,X33] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X34),X33))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X33),X34))
           => ti(X3,X33) = ti(X3,X34) ) ) ),
    c_0_286 ).

fof(c_0_895,axiom,
    ! [X3,X37] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),top_top(fun(X3,bool))))
     => ( hAPP(fun(X3,bool),fun(X3,bool),hAPP(fun(X3,X3),fun(fun(X3,bool),fun(X3,bool)),image(X3,X3),X37),top_top(fun(X3,bool))) = top_top(fun(X3,bool))
       => hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X3),fun(fun(X3,bool),bool),inj_on(X3,X3),X37),top_top(fun(X3,bool)))) ) ),
    c_0_287 ).

fof(c_0_896,axiom,
    ! [X3] :
      ( preorder(X3)
     => ! [X11,X6,X7] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X6),X7))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X7),X6))
           => hBOOL(X11) ) ) ),
    c_0_288 ).

fof(c_0_897,plain,
    ! [X3] :
      ( linorder(X3)
     => ! [X34,X33] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X34),X33))
         => ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X34)) ) ),
    inference(fof_simplification,[status(thm)],[c_0_289]) ).

fof(c_0_898,plain,
    ! [X3] :
      ( linorder(X3)
     => ! [X6,X7] :
          ( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X6),X7))
        <=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X7),X6)) ) ),
    inference(fof_simplification,[status(thm)],[c_0_290]) ).

fof(c_0_899,plain,
    ! [X3] :
      ( linorder(X3)
     => ! [X6,X7] :
          ( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X6),X7))
        <=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X7),X6)) ) ),
    inference(fof_simplification,[status(thm)],[c_0_291]) ).

fof(c_0_900,plain,
    ! [X3] :
      ( linorder(X3)
     => ! [X6,X7] :
          ( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X6),X7))
        <=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X7),X6))
            | ti(X3,X6) = ti(X3,X7) ) ) ),
    inference(fof_simplification,[status(thm)],[c_0_292]) ).

fof(c_0_901,plain,
    ! [X3] :
      ( preorder(X3)
     => ! [X33,X34] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X34))
         => ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X34),X33)) ) ),
    inference(fof_simplification,[status(thm)],[c_0_293]) ).

fof(c_0_902,plain,
    ! [X3] :
      ( preorder(X3)
     => ! [X33,X34] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X34))
         => ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X34),X33)) ) ),
    inference(fof_simplification,[status(thm)],[c_0_294]) ).

fof(c_0_903,plain,
    ! [X3] :
      ( preorder(X3)
     => ! [X21,X22] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X22))
         => ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X22),X21)) ) ),
    inference(fof_simplification,[status(thm)],[c_0_295]) ).

fof(c_0_904,plain,
    ! [X3] :
      ( order(X3)
     => ! [X22,X21] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X22),X21))
         => ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X22)) ) ),
    inference(fof_simplification,[status(thm)],[c_0_296]) ).

fof(c_0_905,plain,
    ! [X3] :
      ( preorder(X3)
     => ! [X33,X34] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X34))
         => ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X34),X33)) ) ),
    inference(fof_simplification,[status(thm)],[c_0_297]) ).

fof(c_0_906,axiom,
    ! [X51,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X51),X53))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),hAPP(nat,nat,suc,X53))) ),
    c_0_298 ).

fof(c_0_907,axiom,
    ! [X51,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),X53))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),hAPP(nat,nat,suc,X53))) ),
    c_0_299 ).

fof(c_0_908,axiom,
    ! [X51,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X51),X53))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X51),hAPP(nat,nat,suc,X53))) ),
    c_0_300 ).

fof(c_0_909,axiom,
    ! [X3] :
      ( linordered_semidom(X3)
     => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),one_one(X3)),one_one(X3)))) ),
    c_0_301 ).

fof(c_0_910,axiom,
    ! [X51,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X51),X53))
     => ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X53),X51))
       => X51 = X53 ) ),
    c_0_302 ).

fof(c_0_911,axiom,
    ! [X3] :
      ( linordered_semidom(X3)
     => ! [X21] : hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),one_one(X3)))) ),
    c_0_303 ).

fof(c_0_912,axiom,
    ! [X3] :
      ( comm_semiring_1(X3)
     => ! [X21,X36,X45] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X36),X45)) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X36),hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X45)) ),
    c_0_304 ).

fof(c_0_913,axiom,
    ! [X3] :
      ( dense_linorder(X3)
     => ! [X35,X34] :
          ( ! [X26] :
              ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X26),X34))
             => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X26),X35)) )
         => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X34),X35)) ) ),
    c_0_305 ).

fof(c_0_914,axiom,
    ! [X3,X39] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X3,bool),nat,finite_card(X3),X39)))
     => hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39)) ),
    c_0_306 ).

fof(c_0_915,axiom,
    ! [X3,X39,X43] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X43))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43))
       => hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39)) ) ),
    c_0_307 ).

fof(c_0_916,axiom,
    ! [X3,X39,X43] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43))
     => ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X43))
       => hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39)) ) ),
    c_0_308 ).

fof(c_0_917,axiom,
    ! [X53,X51] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X53),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X53),X51))),
    c_0_309 ).

fof(c_0_918,axiom,
    ! [X53,X51] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X53),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),X53))),
    c_0_310 ).

fof(c_0_919,axiom,
    ! [X33,X34,X35] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X33),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X34),X35)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X34),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X33),X35)),
    c_0_311 ).

fof(c_0_920,plain,
    ! [X29,X11] :
      ( ~ hBOOL(hAPP(nat,bool,X11,zero_zero(nat)))
     => ( hBOOL(hAPP(nat,bool,X11,X29))
       => ? [X62] :
            ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X62),X29))
            & ! [X16] :
                ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X16),X62))
               => ~ hBOOL(hAPP(nat,bool,X11,X16)) )
            & hBOOL(hAPP(nat,bool,X11,X62)) ) ) ),
    inference(fof_simplification,[status(thm)],[c_0_312]) ).

fof(c_0_921,axiom,
    ! [X3,X50,X11,X6] :
      ( hBOOL(hAPP(X3,bool,X11,X6))
     => ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X11),X50))
       => hBOOL(hAPP(X3,bool,X50,X6)) ) ),
    c_0_313 ).

fof(c_0_922,axiom,
    ! [X3,X6,X11,X50] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X11),X50))
     => ( hBOOL(hAPP(X3,bool,X11,X6))
       => hBOOL(hAPP(X3,bool,X50,X6)) ) ),
    c_0_314 ).

fof(c_0_923,plain,
    ! [X3,X39] :
      ( ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),top_top(fun(X3,bool))))
     => ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39))
       => ? [X19] : ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X19),X39)) ) ),
    inference(fof_simplification,[status(thm)],[c_0_315]) ).

fof(c_0_924,axiom,
    ! [X54,X29] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X29))
    <=> ? [X62] : X29 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),X62)) ),
    c_0_316 ).

fof(c_0_925,axiom,
    ! [X3,X2,X1,X86,X87,X88] : hAPP(X3,X2,hAPP(fun(X3,X1),fun(X3,X2),hAPP(fun(X3,fun(X1,X2)),fun(fun(X3,X1),fun(X3,X2)),combs(X3,X1,X2),X86),X87),X88) = hAPP(X1,X2,hAPP(X3,fun(X1,X2),X86,X88),hAPP(X3,X1,X87,X88)),
    c_0_317 ).

fof(c_0_926,axiom,
    ! [X58,X52] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X58),X52))
     => ( X52 != hAPP(nat,nat,suc,X58)
       => ~ ! [X64] :
              ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X58),X64))
             => X52 != hAPP(nat,nat,suc,X64) ) ) ),
    c_0_318 ).

fof(c_0_927,axiom,
    ! [X51,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),X53))
     => ? [X62] : X53 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),X62)) ),
    c_0_319 ).

fof(c_0_928,axiom,
    ! [X3] :
      ( ring_char_0(X3)
     => ! [X14] :
          ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X14),ring_1_Ints(X3)))
         => ( hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X14),X14) = zero_zero(X3)
          <=> ti(X3,X14) = zero_zero(X3) ) ) ),
    c_0_320 ).

fof(c_0_929,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X36,X21,X22] :
          ( ti(X3,X21) = ti(X3,X22)
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X36),X22))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X36),X21)) ) ) ),
    c_0_321 ).

fof(c_0_930,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X36,X22,X21] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X22),X21))
         => ( ti(X3,X22) = ti(X3,X36)
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X36),X21)) ) ) ),
    c_0_322 ).

fof(c_0_931,plain,
    ! [X3] :
      ( linorder(X3)
     => ! [X7,X6] :
          ( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X7),X6))
         => ( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X6),X7))
          <=> ti(X3,X6) = ti(X3,X7) ) ) ),
    inference(fof_simplification,[status(thm)],[c_0_323]) ).

fof(c_0_932,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X36,X21,X22] :
          ( ti(X3,X21) = ti(X3,X22)
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X36),X22))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X36),X21)) ) ) ),
    c_0_324 ).

fof(c_0_933,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X36,X22,X21] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X22),X21))
         => ( ti(X3,X22) = ti(X3,X36)
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X36),X21)) ) ) ),
    c_0_325 ).

fof(c_0_934,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X22,X21] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X22),X21))
         => ( ti(X3,X21) != ti(X3,X22)
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X22),X21)) ) ) ),
    c_0_326 ).

fof(c_0_935,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X21,X22] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X21),X22))
         => ( ti(X3,X21) != ti(X3,X22)
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X22)) ) ) ),
    c_0_327 ).

fof(c_0_936,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X33,X34] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X33),X34))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X34))
            | ti(X3,X33) = ti(X3,X34) ) ) ),
    c_0_328 ).

fof(c_0_937,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X21,X22] :
          ( ti(X3,X21) != ti(X3,X22)
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X22),X21))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X22),X21)) ) ) ),
    c_0_329 ).

fof(c_0_938,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X21,X22] :
          ( ti(X3,X21) != ti(X3,X22)
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X21),X22))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X22)) ) ) ),
    c_0_330 ).

fof(c_0_939,plain,
    ! [X3] :
      ( linorder(X3)
     => ! [X6,X7] :
          ( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X6),X7))
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X6),X7))
          <=> ti(X3,X6) = ti(X3,X7) ) ) ),
    inference(fof_simplification,[status(thm)],[c_0_331]) ).

fof(c_0_940,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X6,X7] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X6),X7))
        <=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X6),X7))
            | ti(X3,X6) = ti(X3,X7) ) ) ),
    c_0_332 ).

fof(c_0_941,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X6,X7] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X6),X7))
        <=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X6),X7))
            & ti(X3,X6) != ti(X3,X7) ) ) ),
    c_0_333 ).

fof(c_0_942,axiom,
    ! [X3,X1,X6,X7,X37] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),top_top(fun(X3,bool))))
     => ( hAPP(X3,X1,X37,X6) = hAPP(X3,X1,X37,X7)
       => ti(X3,X6) = ti(X3,X7) ) ),
    c_0_334 ).

fof(c_0_943,axiom,
    ! [X3,X1,X6,X7,X37] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),top_top(fun(X3,bool))))
     => ( hAPP(X3,X1,X37,X6) = hAPP(X3,X1,X37,X7)
      <=> ti(X3,X6) = ti(X3,X7) ) ),
    c_0_335 ).

fof(c_0_944,axiom,
    ! [X3] :
      ( ord(X3)
     => ! [X36,X21,X22] :
          ( X21 = X22
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X22),X36))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X21),X36)) ) ) ),
    c_0_336 ).

fof(c_0_945,axiom,
    ! [X3] :
      ( ord(X3)
     => ! [X36,X21,X22] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X21),X22))
         => ( X22 = X36
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X21),X36)) ) ) ),
    c_0_337 ).

fof(c_0_946,axiom,
    ! [X3] :
      ( ord(X3)
     => ! [X36,X21,X22] :
          ( X21 = X22
         => ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X22),X36))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X36)) ) ) ),
    c_0_338 ).

fof(c_0_947,axiom,
    ! [X3] :
      ( ord(X3)
     => ! [X36,X21,X22] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X22))
         => ( X22 = X36
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X21),X36)) ) ) ),
    c_0_339 ).

fof(c_0_948,axiom,
    ! [X3] :
      ( preorder(X3)
     => ! [X33,X34] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X34))
         => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X33),X34)) ) ),
    c_0_340 ).

fof(c_0_949,axiom,
    ! [X77,X66] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X77),X66))),
    c_0_341 ).

fof(c_0_950,axiom,
    ! [X58,X59] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X58),X59))
     => ? [X62] :
          ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X62))
          & hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X58),X62) = X59 ) ),
    c_0_342 ).

fof(c_0_951,axiom,
    ! [X1,X2,X3,X28,X14,X15] : hAPP(product_prod(X1,X2),X3,hAPP(fun(X1,fun(X2,X3)),fun(product_prod(X1,X2),X3),product_prod_rec(X1,X2,X3),X28),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X14),X15)) = hAPP(X2,X3,hAPP(X1,fun(X2,X3),X28,X14),X15),
    c_0_343 ).

fof(c_0_952,axiom,
    ! [X51,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X51),X53))
     => ( X51 != X53
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),X53)) ) ),
    c_0_344 ).

fof(c_0_953,axiom,
    ! [X54,X29] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X29))
    <=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X29))
        | X54 = X29 ) ),
    c_0_345 ).

fof(c_0_954,axiom,
    ! [X54,X29] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X29))
    <=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X29))
        & X54 != X29 ) ),
    c_0_346 ).

fof(c_0_955,axiom,
    ! [X33,X34] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X33),X34))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X33),X34)) ),
    c_0_347 ).

fof(c_0_956,axiom,
    ! [X51,X53] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),X53))
        | X51 = X53 )
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X51),X53)) ),
    c_0_348 ).

fof(c_0_957,axiom,
    ! [X51,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),X53))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X51),X53)) ),
    c_0_349 ).

fof(c_0_958,axiom,
    ! [X29] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X29),hAPP(nat,nat,suc,zero_zero(nat))))
    <=> X29 = zero_zero(nat) ),
    c_0_350 ).

fof(c_0_959,axiom,
    ! [X3] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),top_top(fun(X3,bool))))
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X3,bool),nat,finite_card(X3),top_top(fun(X3,bool))))) ),
    c_0_351 ).

fof(c_0_960,axiom,
    ? [X65] : hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X65),arrow_2064824852le_Lin)),
    c_0_352 ).

fof(c_0_961,axiom,
    hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),lba),arrow_2064824852le_Lin)),
    c_0_353 ).

fof(c_0_962,axiom,
    hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),lab),arrow_2064824852le_Lin)),
    c_0_354 ).

fof(c_0_963,axiom,
    ! [X29,X11] :
      ( hBOOL(hAPP(nat,bool,X11,zero_zero(nat)))
     => ( ! [X44] :
            ( hBOOL(hAPP(nat,bool,X11,X44))
           => hBOOL(hAPP(nat,bool,X11,hAPP(nat,nat,suc,X44))) )
       => hBOOL(hAPP(nat,bool,X11,X29)) ) ),
    c_0_355 ).

fof(c_0_964,axiom,
    ! [X3,X2,X1,X86,X87,X88] : hAPP(X3,X2,hAPP(X1,fun(X3,X2),hAPP(fun(X3,fun(X1,X2)),fun(X1,fun(X3,X2)),combc(X3,X1,X2),X86),X87),X88) = hAPP(X1,X2,hAPP(X3,fun(X1,X2),X86,X88),X87),
    c_0_356 ).

fof(c_0_965,axiom,
    ! [X3,X2,X1,X86,X87,X88] : hAPP(X3,X2,hAPP(fun(X3,X1),fun(X3,X2),hAPP(fun(X1,X2),fun(fun(X3,X1),fun(X3,X2)),combb(X1,X2,X3),X86),X87),X88) = hAPP(X1,X2,X86,hAPP(X3,X1,X87,X88)),
    c_0_357 ).

fof(c_0_966,axiom,
    ! [X51,X53] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,X51)),X53) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),X53)),
    c_0_358 ).

fof(c_0_967,axiom,
    ! [X3,X6,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X39))
    <=> hBOOL(hAPP(X3,bool,X39,X6)) ),
    c_0_359 ).

fof(c_0_968,axiom,
    ! [X54,X29] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X29))
    <=> ? [X62] : X29 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),X62) ),
    c_0_360 ).

fof(c_0_969,plain,
    ! [X3] :
      ( linordered_idom(X3)
     => ! [X33,X34] :
          ( ti(X3,X33) != ti(X3,X34)
         => ( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X34))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X34),X33)) ) ) ),
    inference(fof_simplification,[status(thm)],[c_0_361]) ).

fof(c_0_970,axiom,
    ! [X3] :
      ( linorder(X3)
     => ! [X6,X7] :
          ( ti(X3,X6) != ti(X3,X7)
        <=> ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X6),X7))
            | hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X7),X6)) ) ) ),
    c_0_362 ).

fof(c_0_971,axiom,
    ! [X3] :
      ( linorder(X3)
     => ! [X33,X34] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X34))
          | ti(X3,X33) = ti(X3,X34)
          | hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X34),X33)) ) ),
    c_0_363 ).

fof(c_0_972,plain,
    ! [X3] :
      ( linorder(X3)
     => ! [X33,X34] :
          ( ti(X3,X33) != ti(X3,X34)
         => ( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X34))
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X34),X33)) ) ) ),
    inference(fof_simplification,[status(thm)],[c_0_364]) ).

fof(c_0_973,plain,
    ! [X3] :
      ( linorder(X3)
     => ! [X33,X34] :
          ( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X34))
         => ( ti(X3,X33) != ti(X3,X34)
           => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X34),X33)) ) ) ),
    inference(fof_simplification,[status(thm)],[c_0_365]) ).

fof(c_0_974,plain,
    ! [X3] :
      ( linorder(X3)
     => ! [X34,X33] :
          ( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X34),X33))
         => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X34)) ) ),
    inference(fof_simplification,[status(thm)],[c_0_366]) ).

fof(c_0_975,plain,
    ! [X3] :
      ( linorder(X3)
     => ! [X33,X34] :
          ( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X34))
         => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X34),X33)) ) ),
    inference(fof_simplification,[status(thm)],[c_0_367]) ).

fof(c_0_976,axiom,
    ! [X3] :
      ( linorder(X3)
     => ! [X33,X34] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X33),X34))
          | hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X34),X33)) ) ),
    c_0_368 ).

fof(c_0_977,axiom,
    ! [X3] :
      ( linorder(X3)
     => ! [X33,X34] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X33),X34))
          | hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X34),X33)) ) ),
    c_0_369 ).

fof(c_0_978,plain,
    ! [X3] :
      ( linorder(X3)
     => ! [X33,X34] :
          ( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X33),X34))
         => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X34),X33)) ) ),
    inference(fof_simplification,[status(thm)],[c_0_370]) ).

fof(c_0_979,axiom,
    ! [X29,X60] :
      ( ! [X26] :
          ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X26),X60))
         => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X26),X29)) )
     => hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X60)) ),
    c_0_371 ).

fof(c_0_980,axiom,
    ! [X3,X1] :
      ( hBOOL(hAPP(fun(sum_sum(X3,X1),bool),bool,finite_finite_1(sum_sum(X3,X1)),top_top(fun(sum_sum(X3,X1),bool))))
    <=> ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),top_top(fun(X3,bool))))
        & hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool)))) ) ),
    c_0_372 ).

fof(c_0_981,axiom,
    ! [X1,X3] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),top_top(fun(X3,bool))))
     => ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool))))
       => hBOOL(hAPP(fun(product_prod(X3,X1),bool),bool,finite_finite_1(product_prod(X3,X1)),top_top(fun(product_prod(X3,X1),bool)))) ) ),
    c_0_373 ).

fof(c_0_982,plain,
    ! [X33,X34] :
      ( X33 != X34
     => ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X33),X34))
       => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X34),X33)) ) ),
    inference(fof_simplification,[status(thm)],[c_0_374]) ).

fof(c_0_983,axiom,
    ! [X54,X29] :
      ( X54 != X29
    <=> ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X29))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X29),X54)) ) ),
    c_0_375 ).

fof(c_0_984,axiom,
    ! [X51,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X51),X53))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X53),X51)) ),
    c_0_376 ).

fof(c_0_985,axiom,
    ! [X1,X3,X14,X15,X12,X13] :
      ( hAPP(X1,product_prod(X3,X1),hAPP(X3,fun(X1,product_prod(X3,X1)),product_Pair(X3,X1),X14),X15) = hAPP(X1,product_prod(X3,X1),hAPP(X3,fun(X1,product_prod(X3,X1)),product_Pair(X3,X1),X12),X13)
    <=> ( ti(X3,X14) = ti(X3,X12)
        & ti(X1,X15) = ti(X1,X13) ) ),
    c_0_377 ).

fof(c_0_986,axiom,
    ! [X1,X3,X21,X22,X23,X24] :
      ( hAPP(X1,product_prod(X3,X1),hAPP(X3,fun(X1,product_prod(X3,X1)),product_Pair(X3,X1),X21),X22) = hAPP(X1,product_prod(X3,X1),hAPP(X3,fun(X1,product_prod(X3,X1)),product_Pair(X3,X1),X23),X24)
     => ~ ( ti(X3,X21) = ti(X3,X23)
         => ti(X1,X22) != ti(X1,X24) ) ),
    c_0_378 ).

fof(c_0_987,axiom,
    ! [X3,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39))
     => ( ( ? [X26] : hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X26),X39))
         => one_one(nat) = zero_zero(nat) )
       => hAPP(fun(X3,bool),nat,finite_card(X3),X39) = zero_zero(nat) ) ),
    c_0_379 ).

fof(c_0_988,axiom,
    ! [X51,X53] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),hAPP(nat,nat,suc,X53)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),X53)),
    c_0_380 ).

fof(c_0_989,axiom,
    ! [X51,X53] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,X51)),X53) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),hAPP(nat,nat,suc,X53)),
    c_0_381 ).

fof(c_0_990,axiom,
    ! [X3,X1] :
      ( hBOOL(hAPP(fun(fun(X3,X1),bool),bool,finite_finite_1(fun(X3,X1)),top_top(fun(fun(X3,X1),bool))))
     => ( hAPP(fun(X1,bool),nat,finite_card(X1),top_top(fun(X1,bool))) != hAPP(nat,nat,suc,zero_zero(nat))
       => hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),top_top(fun(X3,bool)))) ) ),
    c_0_382 ).

fof(c_0_991,axiom,
    ! [X3,X1,X37] :
      ( ! [X26,X46] :
          ( hAPP(X3,X1,X37,X26) = hAPP(X3,X1,X37,X46)
         => ti(X3,X26) = ti(X3,X46) )
     => hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X37),top_top(fun(X3,bool)))) ),
    c_0_383 ).

fof(c_0_992,axiom,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),n),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool))))),
    c_0_384 ).

fof(c_0_993,axiom,
    ! [X11,X57] :
      ( hBOOL(hAPP(nat,bool,X11,X57))
     => ( ! [X44] :
            ( hBOOL(hAPP(nat,bool,X11,hAPP(nat,nat,suc,X44)))
           => hBOOL(hAPP(nat,bool,X11,X44)) )
       => hBOOL(hAPP(nat,bool,X11,zero_zero(nat))) ) ),
    c_0_385 ).

fof(c_0_994,axiom,
    ! [X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X53))
     => ? [X32] : X53 = hAPP(nat,nat,suc,X32) ),
    c_0_386 ).

fof(c_0_995,axiom,
    ! [X29] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X29))
    <=> ? [X32] : X29 = hAPP(nat,nat,suc,X32) ),
    c_0_387 ).

fof(c_0_996,axiom,
    ~ ! [X78] :
        ( hBOOL(hAPP(fun(arrow_660593299e_indi,bool),bool,hAPP(fun(arrow_660593299e_indi,nat),fun(fun(arrow_660593299e_indi,bool),bool),inj_on(arrow_660593299e_indi,nat),X78),top_top(fun(arrow_660593299e_indi,bool))))
       => hAPP(fun(arrow_660593299e_indi,bool),fun(nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(fun(arrow_660593299e_indi,bool),fun(nat,bool)),image(arrow_660593299e_indi,nat),X78),top_top(fun(arrow_660593299e_indi,bool))) != hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool)))) ),
    c_0_388 ).

fof(c_0_997,axiom,
    hAPP(fun(arrow_660593299e_indi,bool),fun(nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(fun(arrow_660593299e_indi,bool),fun(nat,bool)),image(arrow_660593299e_indi,nat),h),top_top(fun(arrow_660593299e_indi,bool))) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool)))),
    c_0_389 ).

fof(c_0_998,axiom,
    ! [X3,X1,X39] : hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool)),pi(X3,X1),X39),hAPP(fun(X1,bool),fun(X3,fun(X1,bool)),combk(fun(X1,bool),X3),top_top(fun(X1,bool)))) = top_top(fun(fun(X3,X1),bool)),
    c_0_390 ).

fof(c_0_999,plain,
    ! [X3] :
      ( linordered_semidom(X3)
     => ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),one_one(X3)),zero_zero(X3))) ),
    inference(fof_simplification,[status(thm)],[c_0_391]) ).

fof(c_0_1000,plain,
    ! [X3] :
      ( linordered_semidom(X3)
     => ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),one_one(X3)),zero_zero(X3))) ),
    inference(fof_simplification,[status(thm)],[c_0_392]) ).

fof(c_0_1001,axiom,
    ! [X3] :
      ( top(X3)
     => ! [X21] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),top_top(X3)),X21))
         => ti(X3,X21) = top_top(X3) ) ),
    c_0_393 ).

fof(c_0_1002,axiom,
    ! [X3] :
      ( top(X3)
     => ! [X14] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),top_top(X3)),X14))
        <=> ti(X3,X14) = top_top(X3) ) ),
    c_0_394 ).

fof(c_0_1003,axiom,
    ! [X3] :
      ( cancel_semigroup_add(X3)
     => ! [X14,X15,X17] :
          ( hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X14),X15) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X14),X17)
        <=> ti(X3,X15) = ti(X3,X17) ) ),
    c_0_395 ).

fof(c_0_1004,axiom,
    ! [X3] :
      ( cancel_semigroup_add(X3)
     => ! [X15,X14,X17] :
          ( hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X15),X14) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X17),X14)
        <=> ti(X3,X15) = ti(X3,X17) ) ),
    c_0_396 ).

fof(c_0_1005,axiom,
    ! [X3] :
      ( cancel_semigroup_add(X3)
     => ! [X21,X22,X36] :
          ( hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X22) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X36)
         => ti(X3,X22) = ti(X3,X36) ) ),
    c_0_397 ).

fof(c_0_1006,axiom,
    ! [X3] :
      ( cancel146912293up_add(X3)
     => ! [X21,X22,X36] :
          ( hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X22) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X36)
         => ti(X3,X22) = ti(X3,X36) ) ),
    c_0_398 ).

fof(c_0_1007,axiom,
    ! [X3] :
      ( cancel_semigroup_add(X3)
     => ! [X22,X21,X36] :
          ( hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X22),X21) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X36),X21)
         => ti(X3,X22) = ti(X3,X36) ) ),
    c_0_399 ).

fof(c_0_1008,axiom,
    ! [X3] :
      ( top(X3)
     => ! [X14] :
          ( ti(X3,X14) != top_top(X3)
        <=> hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X14),top_top(X3))) ) ),
    c_0_400 ).

fof(c_0_1009,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X33,X34] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X34))
         => ti(X3,X33) != ti(X3,X34) ) ),
    c_0_401 ).

fof(c_0_1010,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X33,X34] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X34))
         => ti(X3,X33) != ti(X3,X34) ) ),
    c_0_402 ).

fof(c_0_1011,axiom,
    ! [X3] :
      ( order(X3)
     => ! [X33,X34] :
          ( hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X34))
         => ti(X3,X34) != ti(X3,X33) ) ),
    c_0_403 ).

fof(c_0_1012,plain,
    ! [X3] :
      ( top(X3)
     => ! [X21] : ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),top_top(X3)),X21)) ),
    inference(fof_simplification,[status(thm)],[c_0_404]) ).

fof(c_0_1013,axiom,
    ! [X53] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,X53))),
    c_0_405 ).

fof(c_0_1014,plain,
    ! [X3,X33,X34] :
      ( ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),fequal(X3),X33),X34))
      | ti(X3,X33) = ti(X3,X34) ),
    inference(fof_simplification,[status(thm)],[c_0_406]) ).

fof(c_0_1015,axiom,
    ! [X53] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X53),hAPP(nat,nat,suc,X53))),
    c_0_407 ).

fof(c_0_1016,plain,
    ! [X3] :
      ( preorder(X3)
     => ! [X33] : ~ hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),X33),X33)) ),
    inference(fof_simplification,[status(thm)],[c_0_408]) ).

fof(c_0_1017,axiom,
    ! [X29] :
      ( X29 != zero_zero(nat)
    <=> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X29)) ),
    c_0_409 ).

fof(c_0_1018,axiom,
    ! [X29] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X29),zero_zero(nat)))
    <=> X29 = zero_zero(nat) ),
    c_0_410 ).

fof(c_0_1019,plain,
    ! [X53] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X53),zero_zero(nat))),
    inference(fof_simplification,[status(thm)],[c_0_411]) ).

fof(c_0_1020,plain,
    ! [X53] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X53),zero_zero(nat))),
    inference(fof_simplification,[status(thm)],[c_0_412]) ).

fof(c_0_1021,plain,
    ! [X53] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X53),zero_zero(nat))),
    inference(fof_simplification,[status(thm)],[c_0_413]) ).

fof(c_0_1022,axiom,
    ! [X51,X53] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X51),X53))
     => X53 != zero_zero(nat) ),
    c_0_414 ).

fof(c_0_1023,axiom,
    ! [X55,X56] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X55),X56))
     => X55 != X56 ),
    c_0_415 ).

fof(c_0_1024,axiom,
    ! [X53,X51] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X53),X51))
     => X51 != X53 ),
    c_0_416 ).

fof(c_0_1025,plain,
    ! [X53] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X53),X53)),
    inference(fof_simplification,[status(thm)],[c_0_417]) ).

fof(c_0_1026,plain,
    ! [X53] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X53),X53)),
    inference(fof_simplification,[status(thm)],[c_0_418]) ).

fof(c_0_1027,axiom,
    ! [X54,X57,X29] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),X57) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X29),X57)
    <=> X54 = X29 ),
    c_0_419 ).

fof(c_0_1028,axiom,
    ! [X57,X54,X29] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X57),X54) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X57),X29)
    <=> X54 = X29 ),
    c_0_420 ).

fof(c_0_1029,plain,
    ! [X86,X87] :
      ( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X86),X87))
      | hBOOL(X86)
      | hBOOL(X87) ),
    inference(fof_simplification,[status(thm)],[c_0_421]) ).

fof(c_0_1030,plain,
    ! [X86,X87] :
      ( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X86),X87))
      | hBOOL(X87) ),
    inference(fof_simplification,[status(thm)],[c_0_422]) ).

fof(c_0_1031,plain,
    ! [X86,X87] :
      ( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X86),X87))
      | hBOOL(X86) ),
    inference(fof_simplification,[status(thm)],[c_0_423]) ).

fof(c_0_1032,axiom,
    ! [X3,X1,X37,X38] :
      ( ! [X26] : hAPP(X3,X1,X37,X26) = hAPP(X3,X1,X38,X26)
     => ti(fun(X3,X1),X37) = ti(fun(X3,X1),X38) ),
    c_0_424 ).

fof(c_0_1033,axiom,
    ! [X3,X1] :
      ( hBOOL(hAPP(fun(fun(X3,X1),bool),bool,finite_finite_1(fun(X3,X1)),top_top(fun(fun(X3,X1),bool))))
     => hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool)))) ),
    c_0_425 ).

fof(c_0_1034,axiom,
    ! [X3,X39,X43] :
      ( ti(fun(X3,bool),X39) = ti(fun(X3,bool),X43)
     => hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43)) ),
    c_0_426 ).

fof(c_0_1035,axiom,
    ! [X3,X39,X43] :
      ( ti(fun(X3,bool),X39) = ti(fun(X3,bool),X43)
     => hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X43),X39)) ),
    c_0_427 ).

fof(c_0_1036,plain,
    ! [X3,X39,X43] :
      ( ti(fun(X3,bool),X39) = ti(fun(X3,bool),X43)
     => ~ ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X43))
         => ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X43),X39)) ) ),
    inference(fof_simplification,[status(thm)],[c_0_428]) ).

fof(c_0_1037,axiom,
    ! [X3,X39] : hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),top_top(fun(X3,bool)))),
    c_0_429 ).

fof(c_0_1038,axiom,
    ! [X3,X33,X34] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),hAPP(bool,fun(X3,fun(X3,X3)),if(X3),fFalse),X33),X34) = ti(X3,X34),
    c_0_430 ).

fof(c_0_1039,axiom,
    ! [X3,X33,X34] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),hAPP(bool,fun(X3,fun(X3,X3)),if(X3),fTrue),X33),X34) = ti(X3,X33),
    c_0_431 ).

fof(c_0_1040,axiom,
    ! [X54,X29] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),X29) = hAPP(nat,nat,suc,zero_zero(nat))
    <=> ( ( X54 = hAPP(nat,nat,suc,zero_zero(nat))
          & X29 = zero_zero(nat) )
        | ( X54 = zero_zero(nat)
          & X29 = hAPP(nat,nat,suc,zero_zero(nat)) ) ) ),
    c_0_432 ).

fof(c_0_1041,axiom,
    ! [X54,X29] :
      ( hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),X29)
    <=> ( ( X54 = hAPP(nat,nat,suc,zero_zero(nat))
          & X29 = zero_zero(nat) )
        | ( X54 = zero_zero(nat)
          & X29 = hAPP(nat,nat,suc,zero_zero(nat)) ) ) ),
    c_0_433 ).

fof(c_0_1042,axiom,
    ! [X3,X39] : hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X39),X39)),
    c_0_434 ).

fof(c_0_1043,axiom,
    ! [X3,X39] :
      ( hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),top_top(fun(X3,bool))))
     => ( hAPP(fun(X3,bool),nat,finite_card(X3),X39) = hAPP(fun(X3,bool),nat,finite_card(X3),top_top(fun(X3,bool)))
       => ti(fun(X3,bool),X39) = top_top(fun(X3,bool)) ) ),
    c_0_435 ).

fof(c_0_1044,axiom,
    ! [X3,X39] : hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X3),fun(fun(X3,bool),bool),inj_on(X3,X3),combi(X3)),X39)),
    c_0_436 ).

fof(c_0_1045,axiom,
    hBOOL(hAPP(fun(arrow_660593299e_indi,bool),bool,hAPP(fun(arrow_660593299e_indi,nat),fun(fun(arrow_660593299e_indi,bool),bool),inj_on(arrow_660593299e_indi,nat),h),top_top(fun(arrow_660593299e_indi,bool)))),
    c_0_437 ).

fof(c_0_1046,axiom,
    ! [X3,X1] : ti(fun(fun(X3,fun(X3,X3)),fun(X3,fun(fun(X1,X3),fun(fun(fun(X1,bool),X3),bool)))),finite908156982e_idem(X3,X1)) = finite908156982e_idem(X3,X1),
    c_0_438 ).

fof(c_0_1047,axiom,
    ! [X3,X6] : hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),top_top(fun(X3,bool)))),
    c_0_439 ).

fof(c_0_1048,axiom,
    ! [X3,X6] : hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),top_top(fun(X3,bool)))),
    c_0_440 ).

fof(c_0_1049,axiom,
    ! [X60] : hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,nat),fun(fun(nat,bool),bool),inj_on(nat,nat),suc),X60)),
    c_0_441 ).

fof(c_0_1050,axiom,
    ! [X3] :
      ( ring_1(X3)
     => hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),one_one(X3)),ring_1_Ints(X3))) ),
    c_0_442 ).

fof(c_0_1051,axiom,
    ! [X3] :
      ( ring_1(X3)
     => hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),zero_zero(X3)),ring_1_Ints(X3))) ),
    c_0_443 ).

fof(c_0_1052,axiom,
    ! [X3] :
      ( hBOOL(hAPP(fun(option(X3),bool),bool,finite_finite_1(option(X3)),top_top(fun(option(X3),bool))))
    <=> hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),top_top(fun(X3,bool)))) ),
    c_0_444 ).

fof(c_0_1053,axiom,
    ! [X3,X33,X34] :
      ( ti(X3,X33) != ti(X3,X34)
      | hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),fequal(X3),X33),X34)) ),
    c_0_445 ).

fof(c_0_1054,axiom,
    ! [X3] :
      ( linordered_semidom(X3)
     => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less(X3),zero_zero(X3)),one_one(X3))) ),
    c_0_446 ).

fof(c_0_1055,axiom,
    ! [X3] :
      ( linordered_semidom(X3)
     => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),zero_zero(X3)),one_one(X3))) ),
    c_0_447 ).

fof(c_0_1056,axiom,
    ! [X3] :
      ( comm_semiring_1(X3)
     => ! [X21,X36] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),X36) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X36),X21) ),
    c_0_448 ).

fof(c_0_1057,axiom,
    ! [X3] :
      ( top(X3)
     => ! [X21] : hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X21),top_top(X3))) ),
    c_0_449 ).

fof(c_0_1058,axiom,
    ! [X1,X3] : hAPP(fun(X1,bool),fun(sum_sum(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X1,bool),fun(sum_sum(X3,X1),bool)),sum_Plus(X3,X1),top_top(fun(X3,bool))),top_top(fun(X1,bool))) = top_top(fun(sum_sum(X3,X1),bool)),
    c_0_450 ).

fof(c_0_1059,axiom,
    ! [X3] :
      ( preorder(X3)
     => ! [X33,X34] :
          ( X33 = X34
         => hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X33),X34)) ) ),
    c_0_451 ).

fof(c_0_1060,axiom,
    ! [X3] :
      ( preorder(X3)
     => ! [X33] : hBOOL(hAPP(X3,bool,hAPP(X3,fun(X3,bool),ord_less_eq(X3),X33),X33)) ),
    c_0_452 ).

fof(c_0_1061,axiom,
    ! [X53] :
      ( X53 != zero_zero(nat)
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X53)) ),
    c_0_453 ).

fof(c_0_1062,axiom,
    ! [X53] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),X53)),
    c_0_454 ).

fof(c_0_1063,axiom,
    ! [X53] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),X53)),
    c_0_455 ).

fof(c_0_1064,axiom,
    ! [X51,X53] :
      ( X51 = X53
     => hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X51),X53)) ),
    c_0_456 ).

fof(c_0_1065,axiom,
    ! [X53] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X53),X53)),
    c_0_457 ).

fof(c_0_1066,axiom,
    ! [X51,X53] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),X53) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X53),X51),
    c_0_458 ).

fof(c_0_1067,plain,
    ! [X87,X86] :
      ( ~ hBOOL(X86)
      | ~ hBOOL(X87)
      | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X86),X87)) ),
    inference(fof_simplification,[status(thm)],[c_0_459]) ).

fof(c_0_1068,plain,
    ! [X86,X87] :
      ( ~ hBOOL(X87)
      | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X86),X87)) ),
    inference(fof_simplification,[status(thm)],[c_0_460]) ).

fof(c_0_1069,plain,
    ! [X87,X86] :
      ( ~ hBOOL(X86)
      | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X86),X87)) ),
    inference(fof_simplification,[status(thm)],[c_0_461]) ).

fof(c_0_1070,axiom,
    hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,f)),
    c_0_462 ).

fof(c_0_1071,axiom,
    hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,f)),
    c_0_463 ).

fof(c_0_1072,axiom,
    ! [X3] :
      ( semiri456707255roduct(X3)
     => ! [X15,X14] :
          ( ti(X3,X15) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X15),X14)
        <=> ti(X3,X14) = zero_zero(X3) ) ),
    c_0_464 ).

fof(c_0_1073,axiom,
    ! [X3] :
      ( linord219039673up_add(X3)
     => ! [X14] :
          ( hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X14),X14) = zero_zero(X3)
        <=> ti(X3,X14) = zero_zero(X3) ) ),
    c_0_465 ).

fof(c_0_1074,axiom,
    ! [X3] :
      ( linord219039673up_add(X3)
     => ! [X14] :
          ( zero_zero(X3) = hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X14),X14)
        <=> ti(X3,X14) = zero_zero(X3) ) ),
    c_0_466 ).

fof(c_0_1075,axiom,
    ! [X54,X29] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),X29) = zero_zero(nat)
    <=> ( X54 = zero_zero(nat)
        & X29 = zero_zero(nat) ) ),
    c_0_467 ).

fof(c_0_1076,axiom,
    ! [X51,X53] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),X53) = X51
     => X53 = zero_zero(nat) ),
    c_0_468 ).

fof(c_0_1077,axiom,
    ! [X3,X80] : hAPP(fun(X3,bool),fun(X3,bool),hAPP(fun(X3,X3),fun(fun(X3,bool),fun(X3,bool)),image(X3,X3),combi(X3)),X80) = ti(fun(X3,bool),X80),
    c_0_469 ).

fof(c_0_1078,axiom,
    ! [X53] : hAPP(nat,nat,suc,X53) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),X53),
    c_0_470 ).

fof(c_0_1079,axiom,
    ! [X53] : hAPP(nat,nat,suc,X53) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X53),one_one(nat)),
    c_0_471 ).

fof(c_0_1080,axiom,
    ! [X26] : hAPP(nat,fun(nat,bool),ord_less(nat),X26) = hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X26)),
    c_0_472 ).

fof(c_0_1081,plain,
    ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),top_top(fun(nat,bool)))),
    inference(fof_simplification,[status(thm)],[c_0_473]) ).

fof(c_0_1082,axiom,
    ! [X3] : ti(fun(fun(nat,fun(nat,nat)),fun(fun(X3,nat),fun(nat,fun(fun(X3,bool),nat)))),finite_fold_image(nat,X3)) = finite_fold_image(nat,X3),
    c_0_474 ).

fof(c_0_1083,axiom,
    ti(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool)),arrow_218898985ctator) = arrow_218898985ctator,
    c_0_475 ).

fof(c_0_1084,axiom,
    ti(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),arrow_831799591nimity) = arrow_831799591nimity,
    c_0_476 ).

fof(c_0_1085,axiom,
    ti(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),arrow_2037941124le_IIA) = arrow_2037941124le_IIA,
    c_0_477 ).

fof(c_0_1086,axiom,
    ! [X3] : top_top(fun(X3,bool)) = hAPP(fun(X3,bool),fun(X3,bool),collect(X3),hAPP(bool,fun(X3,bool),combk(bool,X3),fTrue)),
    c_0_478 ).

fof(c_0_1087,axiom,
    ! [X1,X3,X86,X87] : hAPP(X1,X3,hAPP(X3,fun(X1,X3),combk(X3,X1),X86),X87) = ti(X3,X86),
    c_0_479 ).

fof(c_0_1088,axiom,
    ! [X3] :
      ( comm_semiring_1(X3)
     => ! [X21] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),zero_zero(X3)),X21) = ti(X3,X21) ),
    c_0_480 ).

fof(c_0_1089,axiom,
    ! [X3] :
      ( monoid_add(X3)
     => ! [X21] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),zero_zero(X3)),X21) = ti(X3,X21) ),
    c_0_481 ).

fof(c_0_1090,axiom,
    ! [X3] :
      ( comm_monoid_add(X3)
     => ! [X21] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),zero_zero(X3)),X21) = ti(X3,X21) ),
    c_0_482 ).

fof(c_0_1091,axiom,
    ! [X3] :
      ( comm_semiring_1(X3)
     => ! [X21] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),zero_zero(X3)) = ti(X3,X21) ),
    c_0_483 ).

fof(c_0_1092,axiom,
    ! [X3] :
      ( monoid_add(X3)
     => ! [X21] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),zero_zero(X3)) = ti(X3,X21) ),
    c_0_484 ).

fof(c_0_1093,axiom,
    ! [X3] :
      ( comm_monoid_add(X3)
     => ! [X21] : hAPP(X3,X3,hAPP(X3,fun(X3,X3),plus_plus(X3),X21),zero_zero(X3)) = ti(X3,X21) ),
    c_0_485 ).

fof(c_0_1094,plain,
    ! [X3,X39] :
      ( ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39))
     => hAPP(fun(X3,bool),nat,finite_card(X3),X39) = zero_zero(nat) ),
    inference(fof_simplification,[status(thm)],[c_0_486]) ).

fof(c_0_1095,axiom,
    ti(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),arrow_1322701812_below) = arrow_1322701812_below,
    c_0_487 ).

fof(c_0_1096,axiom,
    ti(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),arrow_14103264_above) = arrow_14103264_above,
    c_0_488 ).

fof(c_0_1097,axiom,
    ! [X53] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),X53) = X53,
    c_0_489 ).

fof(c_0_1098,axiom,
    ! [X51] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X51),zero_zero(nat)) = X51,
    c_0_490 ).

fof(c_0_1099,plain,
    ! [X86] :
      ( ~ hBOOL(hAPP(bool,bool,fNot,X86))
      | ~ hBOOL(X86) ),
    inference(fof_simplification,[status(thm)],[c_0_491]) ).

fof(c_0_1100,axiom,
    ! [X67,X68] :
      ( hAPP(nat,nat,suc,X67) = hAPP(nat,nat,suc,X68)
    <=> X67 = X68 ),
    c_0_492 ).

fof(c_0_1101,axiom,
    ! [X33,X34] :
      ( hAPP(nat,nat,suc,X33) = hAPP(nat,nat,suc,X34)
     => X33 = X34 ),
    c_0_493 ).

fof(c_0_1102,axiom,
    ! [X3,X1] : ti(fun(fun(X3,bool),fun(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool))),pi(X3,X1)) = pi(X3,X1),
    c_0_494 ).

fof(c_0_1103,axiom,
    ! [X2,X3,X4,X5] : ti(X2,hAPP(X3,X2,X4,X5)) = hAPP(X3,X2,X4,X5),
    c_0_495 ).

fof(c_0_1104,axiom,
    ! [X3] :
      ( finite_finite(X3)
     => hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),top_top(fun(X3,bool)))) ),
    c_0_496 ).

fof(c_0_1105,axiom,
    hBOOL(hAPP(fun(arrow_660593299e_indi,bool),bool,finite_finite_1(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool)))),
    c_0_497 ).

fof(c_0_1106,axiom,
    ! [X3,X1,X2] : ti(fun(fun(X3,fun(X1,X2)),fun(fun(X3,X1),fun(X3,X2))),combs(X3,X1,X2)) = combs(X3,X1,X2),
    c_0_498 ).

fof(c_0_1107,axiom,
    ! [X3,X6] : hBOOL(hAPP(X3,bool,top_top(fun(X3,bool)),X6)),
    c_0_499 ).

fof(c_0_1108,axiom,
    ! [X3,X2,X4,X5] : hAPP(X3,X2,ti(fun(X3,X2),X4),X5) = hAPP(X3,X2,X4,X5),
    c_0_500 ).

fof(c_0_1109,axiom,
    ! [X3,X1] : ti(fun(fun(X3,bool),fun(fun(X1,bool),fun(sum_sum(X3,X1),bool))),sum_Plus(X3,X1)) = sum_Plus(X3,X1),
    c_0_501 ).

fof(c_0_1110,axiom,
    ! [X3] :
      ( finite_finite(X3)
     => ! [X39] : hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39)) ),
    c_0_502 ).

fof(c_0_1111,axiom,
    ! [X3] :
      ( finite_finite(X3)
     => ! [X39] : hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X39)) ),
    c_0_503 ).

fof(c_0_1112,axiom,
    ! [X3,X2,X4,X5] : hAPP(X3,X2,X4,ti(X3,X5)) = hAPP(X3,X2,X4,X5),
    c_0_504 ).

fof(c_0_1113,axiom,
    ! [X1,X2,X3] : ti(fun(fun(X1,fun(X2,X3)),fun(product_prod(X1,X2),X3)),product_prod_rec(X1,X2,X3)) = product_prod_rec(X1,X2,X3),
    c_0_505 ).

fof(c_0_1114,axiom,
    ! [X3,X1,X2] : ti(fun(fun(X3,fun(X1,X2)),fun(X1,fun(X3,X2))),combc(X3,X1,X2)) = combc(X3,X1,X2),
    c_0_506 ).

fof(c_0_1115,axiom,
    ! [X1,X2,X3] : ti(fun(fun(X1,X2),fun(fun(X3,X1),fun(X3,X2))),combb(X1,X2,X3)) = combb(X1,X2,X3),
    c_0_507 ).

fof(c_0_1116,axiom,
    ! [X86] :
      ( hBOOL(X86)
      | hBOOL(hAPP(bool,bool,fNot,X86)) ),
    c_0_508 ).

fof(c_0_1117,axiom,
    ti(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1427655034_mktop) = arrow_1427655034_mktop,
    c_0_509 ).

fof(c_0_1118,axiom,
    ti(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1278947948_mkbot) = arrow_1278947948_mkbot,
    c_0_510 ).

fof(c_0_1119,axiom,
    ! [X51] : zero_zero(nat) != hAPP(nat,nat,suc,X51),
    c_0_511 ).

fof(c_0_1120,axiom,
    ! [X70] : zero_zero(nat) != hAPP(nat,nat,suc,X70),
    c_0_512 ).

fof(c_0_1121,axiom,
    ! [X51] : hAPP(nat,nat,suc,X51) != zero_zero(nat),
    c_0_513 ).

fof(c_0_1122,axiom,
    ! [X69] : hAPP(nat,nat,suc,X69) != zero_zero(nat),
    c_0_514 ).

fof(c_0_1123,axiom,
    ! [X51] : zero_zero(nat) != hAPP(nat,nat,suc,X51),
    c_0_515 ).

fof(c_0_1124,axiom,
    ! [X51] : hAPP(nat,nat,suc,X51) != zero_zero(nat),
    c_0_516 ).

fof(c_0_1125,axiom,
    ! [X3,X1] : ti(fun(fun(X3,bool),fun(fun(X3,X1),fun(X1,X3))),hilbert_inv_into(X3,X1)) = hilbert_inv_into(X3,X1),
    c_0_517 ).

fof(c_0_1126,axiom,
    ! [X53] : X53 != hAPP(nat,nat,suc,X53),
    c_0_518 ).

fof(c_0_1127,axiom,
    ! [X53] : hAPP(nat,nat,suc,X53) != X53,
    c_0_519 ).

fof(c_0_1128,axiom,
    ! [X3,X1] : ti(fun(fun(product_prod(X3,X1),bool),fun(X3,fun(X1,bool))),in_rel(X3,X1)) = in_rel(X3,X1),
    c_0_520 ).

fof(c_0_1129,axiom,
    ! [X1,X3] : ti(fun(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool))),image(X1,X3)) = image(X1,X3),
    c_0_521 ).

fof(c_0_1130,axiom,
    ! [X3,X11] : hAPP(fun(X3,bool),fun(X3,bool),collect(X3),X11) = ti(fun(X3,bool),X11),
    c_0_522 ).

fof(c_0_1131,axiom,
    ti(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),arrow_1111136790e_Prof) = arrow_1111136790e_Prof,
    c_0_523 ).

fof(c_0_1132,axiom,
    hAPP(fun(product_unit,bool),nat,finite_card(product_unit),top_top(fun(product_unit,bool))) = one_one(nat),
    c_0_524 ).

fof(c_0_1133,axiom,
    ! [X1,X3] :
      ( top(X3)
     => ! [X6] : hAPP(X1,X3,top_top(fun(X1,X3)),X6) = top_top(X3) ),
    c_0_525 ).

fof(c_0_1134,axiom,
    ! [X3,X1] : ti(fun(fun(X3,X1),fun(fun(X3,bool),bool)),inj_on(X3,X1)) = inj_on(X3,X1),
    c_0_526 ).

fof(c_0_1135,axiom,
    ! [X3,X86] : hAPP(X3,X3,combi(X3),X86) = ti(X3,X86),
    c_0_527 ).

fof(c_0_1136,axiom,
    ! [X34] :
      ( X34 != zero_zero(nat)
     => ~ ! [X74] : X34 != hAPP(nat,nat,suc,X74) ),
    c_0_528 ).

fof(c_0_1137,axiom,
    ! [X53] :
      ( X53 != zero_zero(nat)
     => ? [X32] : X53 = hAPP(nat,nat,suc,X32) ),
    c_0_529 ).

fof(c_0_1138,axiom,
    one_one(nat) = hAPP(nat,nat,suc,zero_zero(nat)),
    c_0_530 ).

fof(c_0_1139,axiom,
    ! [X3,X1] : ti(fun(X3,fun(X1,product_prod(X3,X1))),product_Pair(X3,X1)) = product_Pair(X3,X1),
    c_0_531 ).

fof(c_0_1140,axiom,
    ! [X3] : ti(fun(bool,fun(X3,fun(X3,X3))),if(X3)) = if(X3),
    c_0_532 ).

fof(c_0_1141,axiom,
    ! [X3] :
      ( linorder(X3)
     => ti(fun(X3,fun(X3,fun(X3,bool))),ord_atLeastLessThan(X3)) = ord_atLeastLessThan(X3) ),
    c_0_533 ).

fof(c_0_1142,axiom,
    ! [X3] : ti(fun(X3,fun(fun(X3,bool),bool)),member(X3)) = member(X3),
    c_0_534 ).

fof(c_0_1143,axiom,
    ti(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),arrow_2064824852le_Lin) = arrow_2064824852le_Lin,
    c_0_535 ).

fof(c_0_1144,axiom,
    ! [X3] : ti(fun(fun(X3,bool),fun(X3,bool)),collect(X3)) = collect(X3),
    c_0_536 ).

fof(c_0_1145,axiom,
    ! [X3,X1] : ti(fun(X3,fun(X1,X3)),combk(X3,X1)) = combk(X3,X1),
    c_0_537 ).

fof(c_0_1146,axiom,
    ! [X3] :
      ( cancel_semigroup_add(X3)
     => ti(fun(X3,fun(X3,X3)),plus_plus(X3)) = plus_plus(X3) ),
    c_0_538 ).

fof(c_0_1147,axiom,
    ! [X3] :
      ( ab_semigroup_add(X3)
     => ti(fun(X3,fun(X3,X3)),plus_plus(X3)) = plus_plus(X3) ),
    c_0_539 ).

fof(c_0_1148,axiom,
    ! [X3] :
      ( monoid_add(X3)
     => ti(fun(X3,fun(X3,X3)),plus_plus(X3)) = plus_plus(X3) ),
    c_0_540 ).

fof(c_0_1149,axiom,
    ! [X1] :
      ( ord(X1)
     => ti(fun(X1,fun(X1,bool)),ord_less_eq(X1)) = ord_less_eq(X1) ),
    c_0_541 ).

fof(c_0_1150,axiom,
    ! [X3] :
      ( ord(X3)
     => ti(fun(X3,fun(X3,bool)),ord_less(X3)) = ord_less(X3) ),
    c_0_542 ).

fof(c_0_1151,axiom,
    ! [X3] : ti(fun(X3,fun(X3,bool)),fequal(X3)) = fequal(X3),
    c_0_543 ).

fof(c_0_1152,axiom,
    ! [X1] : ti(fun(fun(X1,bool),bool),finite_finite_1(X1)) = finite_finite_1(X1),
    c_0_544 ).

fof(c_0_1153,axiom,
    ! [X3] : ti(fun(fun(X3,bool),nat),finite_card(X3)) = finite_card(X3),
    c_0_545 ).

fof(c_0_1154,axiom,
    ti(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),lba) = lba,
    c_0_546 ).

fof(c_0_1155,axiom,
    ti(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),lab) = lab,
    c_0_547 ).

fof(c_0_1156,axiom,
    ti(fun(bool,fun(bool,bool)),fdisj) = fdisj,
    c_0_548 ).

fof(c_0_1157,axiom,
    ti(fun(bool,fun(bool,bool)),fconj) = fconj,
    c_0_549 ).

fof(c_0_1158,axiom,
    ! [X3] :
      ( ring_1(X3)
     => ti(fun(X3,bool),ring_1_Ints(X3)) = ring_1_Ints(X3) ),
    c_0_550 ).

fof(c_0_1159,axiom,
    ! [X3] :
      ( zero(X3)
     => ! [X6] :
          ( zero_zero(X3) = ti(X3,X6)
        <=> ti(X3,X6) = zero_zero(X3) ) ),
    c_0_551 ).

fof(c_0_1160,axiom,
    ! [X3] :
      ( one(X3)
     => ! [X6] :
          ( one_one(X3) = ti(X3,X6)
        <=> ti(X3,X6) = one_one(X3) ) ),
    c_0_552 ).

fof(c_0_1161,axiom,
    ! [X84,X85] : ti(X84,ti(X84,X85)) = ti(X84,X85),
    c_0_553 ).

fof(c_0_1162,axiom,
    ! [X3] : ti(fun(X3,X3),combi(X3)) = combi(X3),
    c_0_554 ).

fof(c_0_1163,axiom,
    ! [X82,X83] :
      ( ( finite_finite(X83)
        & finite_finite(X82) )
     => finite_finite(product_prod(X82,X83)) ),
    c_0_555 ).

fof(c_0_1164,axiom,
    ! [X82,X83] :
      ( ( finite_finite(X83)
        & finite_finite(X82) )
     => finite_finite(sum_sum(X82,X83)) ),
    c_0_556 ).

fof(c_0_1165,axiom,
    ! [X82,X83] :
      ( ( finite_finite(X83)
        & finite_finite(X82) )
     => finite_finite(fun(X82,X83)) ),
    c_0_557 ).

fof(c_0_1166,axiom,
    ! [X82,X83] :
      ( ord(X83)
     => ord(fun(X82,X83)) ),
    c_0_558 ).

fof(c_0_1167,axiom,
    ! [X82,X83] :
      ( top(X83)
     => top(fun(X82,X83)) ),
    c_0_559 ).

fof(c_0_1168,axiom,
    ! [X82,X83] :
      ( order(X83)
     => order(fun(X82,X83)) ),
    c_0_560 ).

fof(c_0_1169,axiom,
    ! [X82,X83] :
      ( preorder(X83)
     => preorder(fun(X82,X83)) ),
    c_0_561 ).

fof(c_0_1170,axiom,
    ti(fun(arrow_660593299e_indi,nat),h) = h,
    c_0_562 ).

fof(c_0_1171,axiom,
    ti(fun(bool,bool),fNot) = fNot,
    c_0_563 ).

fof(c_0_1172,axiom,
    ti(fun(nat,nat),suc) = suc,
    c_0_564 ).

fof(c_0_1173,axiom,
    ! [X3] :
      ( top(X3)
     => ti(X3,top_top(X3)) = top_top(X3) ),
    c_0_565 ).

fof(c_0_1174,axiom,
    ! [X3] :
      ( zero(X3)
     => ti(X3,zero_zero(X3)) = zero_zero(X3) ),
    c_0_566 ).

fof(c_0_1175,axiom,
    ! [X3] :
      ( one(X3)
     => ti(X3,one_one(X3)) = one_one(X3) ),
    c_0_567 ).

fof(c_0_1176,axiom,
    ! [X86] :
      ( ti(bool,X86) = fTrue
      | ti(bool,X86) = fFalse ),
    c_0_568 ).

fof(c_0_1177,axiom,
    ! [X86] :
      ( ti(bool,X86) = fTrue
      | ti(bool,X86) = fFalse ),
    c_0_569 ).

fof(c_0_1178,axiom,
    ! [X3] : ti(X3,undefined(X3)) = undefined(X3),
    c_0_570 ).

fof(c_0_1179,axiom,
    ! [X3] :
      ( zero_neq_one(X3)
     => one_one(X3) != zero_zero(X3) ),
    c_0_571 ).

fof(c_0_1180,axiom,
    ! [X3] :
      ( zero_neq_one(X3)
     => zero_zero(X3) != one_one(X3) ),
    c_0_572 ).

fof(c_0_1181,axiom,
    ! [X83] :
      ( finite_finite(X83)
     => finite_finite(option(X83)) ),
    c_0_573 ).

fof(c_0_1182,axiom,
    ti(nat,n) = n,
    c_0_574 ).

fof(c_0_1183,axiom,
    ti(arrow_490897120le_alt,e) = e,
    c_0_575 ).

fof(c_0_1184,axiom,
    ti(arrow_490897120le_alt,b) = b,
    c_0_576 ).

fof(c_0_1185,axiom,
    ti(arrow_490897120le_alt,a) = a,
    c_0_577 ).

fof(c_0_1186,axiom,
    ti(bool,fTrue) = fTrue,
    c_0_578 ).

fof(c_0_1187,axiom,
    ti(bool,fFalse) = fFalse,
    c_0_579 ).

fof(c_0_1188,axiom,
    hBOOL(fTrue),
    c_0_580 ).

fof(c_0_1189,axiom,
    finite_finite(product_unit),
    c_0_581 ).

fof(c_0_1190,axiom,
    ord(bool),
    c_0_582 ).

fof(c_0_1191,axiom,
    top(bool),
    c_0_583 ).

fof(c_0_1192,axiom,
    order(bool),
    c_0_584 ).

fof(c_0_1193,axiom,
    finite_finite(bool),
    c_0_585 ).

fof(c_0_1194,axiom,
    preorder(bool),
    c_0_586 ).

fof(c_0_1195,axiom,
    one(nat),
    c_0_587 ).

fof(c_0_1196,axiom,
    zero(nat),
    c_0_588 ).

fof(c_0_1197,axiom,
    ord(nat),
    c_0_589 ).

fof(c_0_1198,axiom,
    order(nat),
    c_0_590 ).

fof(c_0_1199,axiom,
    monoid_add(nat),
    c_0_591 ).

fof(c_0_1200,axiom,
    linorder(nat),
    c_0_592 ).

fof(c_0_1201,axiom,
    preorder(nat),
    c_0_593 ).

fof(c_0_1202,axiom,
    zero_neq_one(nat),
    c_0_594 ).

fof(c_0_1203,axiom,
    comm_semiring_1(nat),
    c_0_595 ).

fof(c_0_1204,axiom,
    comm_monoid_add(nat),
    c_0_596 ).

fof(c_0_1205,axiom,
    ab_semigroup_add(nat),
    c_0_597 ).

fof(c_0_1206,axiom,
    linordered_semidom(nat),
    c_0_598 ).

fof(c_0_1207,axiom,
    cancel_semigroup_add(nat),
    c_0_599 ).

fof(c_0_1208,axiom,
    cancel146912293up_add(nat),
    c_0_600 ).

fof(c_0_1209,axiom,
    ordere216010020id_add(nat),
    c_0_601 ).

fof(c_0_1210,axiom,
    ordere779506340up_add(nat),
    c_0_602 ).

fof(c_0_1211,axiom,
    ordere236663937imp_le(nat),
    c_0_603 ).

fof(c_0_1212,axiom,
    ordere223160158up_add(nat),
    c_0_604 ).

fof(c_0_1213,axiom,
    semiri456707255roduct(nat),
    c_0_605 ).

fof(c_0_1214,axiom,
    a != b,
    c_0_606 ).

fof(c_0_1215,axiom,
    c != d,
    c_0_607 ).

fof(c_0_1216,plain,
    ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e))))))
      | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))),lab)),lba)))) )
    & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))),lab)),lba))))
      | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))))) ) ),
    inference(fof_nnf,[status(thm)],[c_0_608]) ).

fof(c_0_1217,plain,
    ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e))))))
      | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),lab)),lba)))) )
    & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),lab)),lba))))
      | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))))) ) ),
    inference(fof_nnf,[status(thm)],[c_0_609]) ).

fof(c_0_1218,plain,
    ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,p)))
      | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))))) )
    & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e))))))
      | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,p))) ) ),
    inference(fof_nnf,[status(thm)],[c_0_610]) ).

fof(c_0_1219,axiom,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))))),
    c_0_611 ).

fof(c_0_1220,axiom,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))))),
    c_0_612 ).

fof(c_0_1221,axiom,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))))),
    c_0_613 ).

fof(c_0_1222,axiom,
    hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))),arrow_1111136790e_Prof)),
    c_0_614 ).

fof(c_0_1223,plain,
    ! [X46] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk28_0),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool)))))
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X46),esk28_0))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),X46))),lab)),lba)))) )
      & hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),esk28_0),one_one(nat))))),lab)),lba)))) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_615])])])]) ).

fof(c_0_1224,plain,
    ! [X46] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk27_0),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool)))))
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X46),esk27_0))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),X46))),lab)),lba)))) )
      & hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),esk27_0),one_one(nat))))),lab)),lba)))) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_616])])])]) ).

fof(c_0_1225,axiom,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))),lab)),lba)))),
    c_0_617 ).

fof(c_0_1226,plain,
    ! [X33] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X33),n))
      | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),X33))),lab)),lba)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_618])]) ).

fof(c_0_1227,plain,
    ! [X30] : hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),X30))),lab)),lba)),arrow_1111136790e_Prof)),
    inference(variable_rename,[status(thm)],[c_0_619]) ).

fof(c_0_1228,plain,
    ! [X42,X43,X44,X45,X46,X47,X48,X49] :
      ( ( ~ hBOOL(hAPP(fun(X42,fun(X43,bool)),bool,hAPP(fun(X42,fun(X43,bool)),fun(fun(X42,fun(X43,bool)),bool),ord_less_eq(fun(X42,fun(X43,bool))),hAPP(fun(product_prod(X42,X43),bool),fun(X42,fun(X43,bool)),hAPP(fun(X42,fun(fun(product_prod(X42,X43),bool),fun(X43,bool))),fun(fun(product_prod(X42,X43),bool),fun(X42,fun(X43,bool))),combc(X42,fun(product_prod(X42,X43),bool),fun(X43,bool)),hAPP(fun(X42,fun(X43,fun(fun(product_prod(X42,X43),bool),bool))),fun(X42,fun(fun(product_prod(X42,X43),bool),fun(X43,bool))),hAPP(fun(fun(X43,fun(fun(product_prod(X42,X43),bool),bool)),fun(fun(product_prod(X42,X43),bool),fun(X43,bool))),fun(fun(X42,fun(X43,fun(fun(product_prod(X42,X43),bool),bool))),fun(X42,fun(fun(product_prod(X42,X43),bool),fun(X43,bool)))),combb(fun(X43,fun(fun(product_prod(X42,X43),bool),bool)),fun(fun(product_prod(X42,X43),bool),fun(X43,bool)),X42),combc(X43,fun(product_prod(X42,X43),bool),bool)),hAPP(fun(X42,fun(X43,product_prod(X42,X43))),fun(X42,fun(X43,fun(fun(product_prod(X42,X43),bool),bool))),hAPP(fun(fun(X43,product_prod(X42,X43)),fun(X43,fun(fun(product_prod(X42,X43),bool),bool))),fun(fun(X42,fun(X43,product_prod(X42,X43))),fun(X42,fun(X43,fun(fun(product_prod(X42,X43),bool),bool)))),combb(fun(X43,product_prod(X42,X43)),fun(X43,fun(fun(product_prod(X42,X43),bool),bool)),X42),hAPP(fun(product_prod(X42,X43),fun(fun(product_prod(X42,X43),bool),bool)),fun(fun(X43,product_prod(X42,X43)),fun(X43,fun(fun(product_prod(X42,X43),bool),bool))),combb(product_prod(X42,X43),fun(fun(product_prod(X42,X43),bool),bool),X43),member(product_prod(X42,X43)))),product_Pair(X42,X43)))),X44)),hAPP(fun(product_prod(X42,X43),bool),fun(X42,fun(X43,bool)),hAPP(fun(X42,fun(fun(product_prod(X42,X43),bool),fun(X43,bool))),fun(fun(product_prod(X42,X43),bool),fun(X42,fun(X43,bool))),combc(X42,fun(product_prod(X42,X43),bool),fun(X43,bool)),hAPP(fun(X42,fun(X43,fun(fun(product_prod(X42,X43),bool),bool))),fun(X42,fun(fun(product_prod(X42,X43),bool),fun(X43,bool))),hAPP(fun(fun(X43,fun(fun(product_prod(X42,X43),bool),bool)),fun(fun(product_prod(X42,X43),bool),fun(X43,bool))),fun(fun(X42,fun(X43,fun(fun(product_prod(X42,X43),bool),bool))),fun(X42,fun(fun(product_prod(X42,X43),bool),fun(X43,bool)))),combb(fun(X43,fun(fun(product_prod(X42,X43),bool),bool)),fun(fun(product_prod(X42,X43),bool),fun(X43,bool)),X42),combc(X43,fun(product_prod(X42,X43),bool),bool)),hAPP(fun(X42,fun(X43,product_prod(X42,X43))),fun(X42,fun(X43,fun(fun(product_prod(X42,X43),bool),bool))),hAPP(fun(fun(X43,product_prod(X42,X43)),fun(X43,fun(fun(product_prod(X42,X43),bool),bool))),fun(fun(X42,fun(X43,product_prod(X42,X43))),fun(X42,fun(X43,fun(fun(product_prod(X42,X43),bool),bool)))),combb(fun(X43,product_prod(X42,X43)),fun(X43,fun(fun(product_prod(X42,X43),bool),bool)),X42),hAPP(fun(product_prod(X42,X43),fun(fun(product_prod(X42,X43),bool),bool)),fun(fun(X43,product_prod(X42,X43)),fun(X43,fun(fun(product_prod(X42,X43),bool),bool))),combb(product_prod(X42,X43),fun(fun(product_prod(X42,X43),bool),bool),X43),member(product_prod(X42,X43)))),product_Pair(X42,X43)))),X45)))
        | hBOOL(hAPP(fun(product_prod(X42,X43),bool),bool,hAPP(fun(product_prod(X42,X43),bool),fun(fun(product_prod(X42,X43),bool),bool),ord_less_eq(fun(product_prod(X42,X43),bool)),X44),X45)) )
      & ( ~ hBOOL(hAPP(fun(product_prod(X46,X47),bool),bool,hAPP(fun(product_prod(X46,X47),bool),fun(fun(product_prod(X46,X47),bool),bool),ord_less_eq(fun(product_prod(X46,X47),bool)),X48),X49))
        | hBOOL(hAPP(fun(X46,fun(X47,bool)),bool,hAPP(fun(X46,fun(X47,bool)),fun(fun(X46,fun(X47,bool)),bool),ord_less_eq(fun(X46,fun(X47,bool))),hAPP(fun(product_prod(X46,X47),bool),fun(X46,fun(X47,bool)),hAPP(fun(X46,fun(fun(product_prod(X46,X47),bool),fun(X47,bool))),fun(fun(product_prod(X46,X47),bool),fun(X46,fun(X47,bool))),combc(X46,fun(product_prod(X46,X47),bool),fun(X47,bool)),hAPP(fun(X46,fun(X47,fun(fun(product_prod(X46,X47),bool),bool))),fun(X46,fun(fun(product_prod(X46,X47),bool),fun(X47,bool))),hAPP(fun(fun(X47,fun(fun(product_prod(X46,X47),bool),bool)),fun(fun(product_prod(X46,X47),bool),fun(X47,bool))),fun(fun(X46,fun(X47,fun(fun(product_prod(X46,X47),bool),bool))),fun(X46,fun(fun(product_prod(X46,X47),bool),fun(X47,bool)))),combb(fun(X47,fun(fun(product_prod(X46,X47),bool),bool)),fun(fun(product_prod(X46,X47),bool),fun(X47,bool)),X46),combc(X47,fun(product_prod(X46,X47),bool),bool)),hAPP(fun(X46,fun(X47,product_prod(X46,X47))),fun(X46,fun(X47,fun(fun(product_prod(X46,X47),bool),bool))),hAPP(fun(fun(X47,product_prod(X46,X47)),fun(X47,fun(fun(product_prod(X46,X47),bool),bool))),fun(fun(X46,fun(X47,product_prod(X46,X47))),fun(X46,fun(X47,fun(fun(product_prod(X46,X47),bool),bool)))),combb(fun(X47,product_prod(X46,X47)),fun(X47,fun(fun(product_prod(X46,X47),bool),bool)),X46),hAPP(fun(product_prod(X46,X47),fun(fun(product_prod(X46,X47),bool),bool)),fun(fun(X47,product_prod(X46,X47)),fun(X47,fun(fun(product_prod(X46,X47),bool),bool))),combb(product_prod(X46,X47),fun(fun(product_prod(X46,X47),bool),bool),X47),member(product_prod(X46,X47)))),product_Pair(X46,X47)))),X48)),hAPP(fun(product_prod(X46,X47),bool),fun(X46,fun(X47,bool)),hAPP(fun(X46,fun(fun(product_prod(X46,X47),bool),fun(X47,bool))),fun(fun(product_prod(X46,X47),bool),fun(X46,fun(X47,bool))),combc(X46,fun(product_prod(X46,X47),bool),fun(X47,bool)),hAPP(fun(X46,fun(X47,fun(fun(product_prod(X46,X47),bool),bool))),fun(X46,fun(fun(product_prod(X46,X47),bool),fun(X47,bool))),hAPP(fun(fun(X47,fun(fun(product_prod(X46,X47),bool),bool)),fun(fun(product_prod(X46,X47),bool),fun(X47,bool))),fun(fun(X46,fun(X47,fun(fun(product_prod(X46,X47),bool),bool))),fun(X46,fun(fun(product_prod(X46,X47),bool),fun(X47,bool)))),combb(fun(X47,fun(fun(product_prod(X46,X47),bool),bool)),fun(fun(product_prod(X46,X47),bool),fun(X47,bool)),X46),combc(X47,fun(product_prod(X46,X47),bool),bool)),hAPP(fun(X46,fun(X47,product_prod(X46,X47))),fun(X46,fun(X47,fun(fun(product_prod(X46,X47),bool),bool))),hAPP(fun(fun(X47,product_prod(X46,X47)),fun(X47,fun(fun(product_prod(X46,X47),bool),bool))),fun(fun(X46,fun(X47,product_prod(X46,X47))),fun(X46,fun(X47,fun(fun(product_prod(X46,X47),bool),bool)))),combb(fun(X47,product_prod(X46,X47)),fun(X47,fun(fun(product_prod(X46,X47),bool),bool)),X46),hAPP(fun(product_prod(X46,X47),fun(fun(product_prod(X46,X47),bool),bool)),fun(fun(X47,product_prod(X46,X47)),fun(X47,fun(fun(product_prod(X46,X47),bool),bool))),combb(product_prod(X46,X47),fun(fun(product_prod(X46,X47),bool),bool),X47),member(product_prod(X46,X47)))),product_Pair(X46,X47)))),X49))) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_620])])])]) ).

fof(c_0_1229,plain,
    ! [X72,X73] :
      ( ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),X73))
      | hAPP(nat,nat,suc,hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),hAPP(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool)),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool))),combb(nat,fun(fun(nat,bool),bool),nat),member(nat)),suc)),X73))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X72))))) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),X73))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,X72))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_621])]) ).

fof(c_0_1230,plain,
    ! [X72,X73] :
      ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),X73))
      | hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),hAPP(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool)),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool))),combb(nat,fun(fun(nat,bool),bool),nat),member(nat)),suc)),X73))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X72)))) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),X73))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,X72))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_622])]) ).

fof(c_0_1231,plain,
    ! [X47,X48,X49,X50,X51,X52] :
      ( ( hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less(X47),esk58_6(X47,X48,X49,X50,X51,X52)),esk59_6(X47,X48,X49,X50,X51,X52)))
        | hBOOL(hAPP(X48,bool,hAPP(X48,fun(X48,bool),ord_less(X48),hAPP(X47,X48,X49,X51)),X50))
        | ~ hBOOL(hAPP(X48,bool,hAPP(X48,fun(X48,bool),ord_less_eq(X48),hAPP(X47,X48,X49,X52)),X50))
        | ~ hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less(X47),X51),X52))
        | ~ order(X48)
        | ~ order(X47) )
      & ( ~ hBOOL(hAPP(X48,bool,hAPP(X48,fun(X48,bool),ord_less(X48),hAPP(X47,X48,X49,esk58_6(X47,X48,X49,X50,X51,X52))),hAPP(X47,X48,X49,esk59_6(X47,X48,X49,X50,X51,X52))))
        | hBOOL(hAPP(X48,bool,hAPP(X48,fun(X48,bool),ord_less(X48),hAPP(X47,X48,X49,X51)),X50))
        | ~ hBOOL(hAPP(X48,bool,hAPP(X48,fun(X48,bool),ord_less_eq(X48),hAPP(X47,X48,X49,X52)),X50))
        | ~ hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less(X47),X51),X52))
        | ~ order(X48)
        | ~ order(X47) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_623])])])])]) ).

fof(c_0_1232,plain,
    ! [X47,X48,X49,X50,X51,X52] :
      ( ( hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less_eq(X47),esk48_6(X47,X48,X49,X50,X51,X52)),esk49_6(X47,X48,X49,X50,X51,X52)))
        | hBOOL(hAPP(X48,bool,hAPP(X48,fun(X48,bool),ord_less(X48),hAPP(X47,X48,X49,X51)),X50))
        | ~ hBOOL(hAPP(X48,bool,hAPP(X48,fun(X48,bool),ord_less(X48),hAPP(X47,X48,X49,X52)),X50))
        | ~ hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less_eq(X47),X51),X52))
        | ~ order(X48)
        | ~ order(X47) )
      & ( ~ hBOOL(hAPP(X48,bool,hAPP(X48,fun(X48,bool),ord_less_eq(X48),hAPP(X47,X48,X49,esk48_6(X47,X48,X49,X50,X51,X52))),hAPP(X47,X48,X49,esk49_6(X47,X48,X49,X50,X51,X52))))
        | hBOOL(hAPP(X48,bool,hAPP(X48,fun(X48,bool),ord_less(X48),hAPP(X47,X48,X49,X51)),X50))
        | ~ hBOOL(hAPP(X48,bool,hAPP(X48,fun(X48,bool),ord_less(X48),hAPP(X47,X48,X49,X52)),X50))
        | ~ hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less_eq(X47),X51),X52))
        | ~ order(X48)
        | ~ order(X47) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_624])])])])]) ).

fof(c_0_1233,plain,
    ! [X47,X48,X49,X50,X51,X52] :
      ( ( hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less_eq(X47),esk43_6(X47,X48,X49,X50,X51,X52)),esk42_6(X47,X48,X49,X50,X51,X52)))
        | hBOOL(hAPP(X48,bool,hAPP(X48,fun(X48,bool),ord_less(X48),hAPP(X47,X48,X50,X49)),X52))
        | ~ hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less_eq(X47),X49),X51))
        | ~ hBOOL(hAPP(X48,bool,hAPP(X48,fun(X48,bool),ord_less(X48),hAPP(X47,X48,X50,X51)),X52))
        | ~ order(X48)
        | ~ order(X47) )
      & ( ~ hBOOL(hAPP(X48,bool,hAPP(X48,fun(X48,bool),ord_less_eq(X48),hAPP(X47,X48,X50,esk43_6(X47,X48,X49,X50,X51,X52))),hAPP(X47,X48,X50,esk42_6(X47,X48,X49,X50,X51,X52))))
        | hBOOL(hAPP(X48,bool,hAPP(X48,fun(X48,bool),ord_less(X48),hAPP(X47,X48,X50,X49)),X52))
        | ~ hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less_eq(X47),X49),X51))
        | ~ hBOOL(hAPP(X48,bool,hAPP(X48,fun(X48,bool),ord_less(X48),hAPP(X47,X48,X50,X51)),X52))
        | ~ order(X48)
        | ~ order(X47) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_625])])])])]) ).

fof(c_0_1234,plain,
    ! [X47,X48,X49,X50,X51,X52] :
      ( ( hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less(X47),esk41_6(X47,X48,X49,X50,X51,X52)),esk40_6(X47,X48,X49,X50,X51,X52)))
        | hBOOL(hAPP(X48,bool,hAPP(X48,fun(X48,bool),ord_less(X48),hAPP(X47,X48,X50,X49)),X52))
        | ~ hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less(X47),X49),X51))
        | ~ hBOOL(hAPP(X48,bool,hAPP(X48,fun(X48,bool),ord_less_eq(X48),hAPP(X47,X48,X50,X51)),X52))
        | ~ order(X48)
        | ~ ord(X47) )
      & ( ~ hBOOL(hAPP(X48,bool,hAPP(X48,fun(X48,bool),ord_less(X48),hAPP(X47,X48,X50,esk41_6(X47,X48,X49,X50,X51,X52))),hAPP(X47,X48,X50,esk40_6(X47,X48,X49,X50,X51,X52))))
        | hBOOL(hAPP(X48,bool,hAPP(X48,fun(X48,bool),ord_less(X48),hAPP(X47,X48,X50,X49)),X52))
        | ~ hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less(X47),X49),X51))
        | ~ hBOOL(hAPP(X48,bool,hAPP(X48,fun(X48,bool),ord_less_eq(X48),hAPP(X47,X48,X50,X51)),X52))
        | ~ order(X48)
        | ~ ord(X47) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_626])])])])]) ).

fof(c_0_1235,plain,
    ! [X47,X48,X49,X50,X51,X52] :
      ( ( hBOOL(hAPP(X48,bool,hAPP(X48,fun(X48,bool),ord_less_eq(X48),esk57_6(X47,X48,X49,X50,X51,X52)),esk56_6(X47,X48,X49,X50,X51,X52)))
        | hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less(X47),X49),hAPP(X48,X47,X50,X52)))
        | ~ hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less(X47),X49),hAPP(X48,X47,X50,X51)))
        | ~ hBOOL(hAPP(X48,bool,hAPP(X48,fun(X48,bool),ord_less_eq(X48),X51),X52))
        | ~ order(X48)
        | ~ order(X47) )
      & ( ~ hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less_eq(X47),hAPP(X48,X47,X50,esk57_6(X47,X48,X49,X50,X51,X52))),hAPP(X48,X47,X50,esk56_6(X47,X48,X49,X50,X51,X52))))
        | hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less(X47),X49),hAPP(X48,X47,X50,X52)))
        | ~ hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less(X47),X49),hAPP(X48,X47,X50,X51)))
        | ~ hBOOL(hAPP(X48,bool,hAPP(X48,fun(X48,bool),ord_less_eq(X48),X51),X52))
        | ~ order(X48)
        | ~ order(X47) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_627])])])])]) ).

fof(c_0_1236,plain,
    ! [X47,X48,X49,X50,X51,X52] :
      ( ( hBOOL(hAPP(X48,bool,hAPP(X48,fun(X48,bool),ord_less(X48),esk55_6(X47,X48,X49,X50,X51,X52)),esk54_6(X47,X48,X49,X50,X51,X52)))
        | hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less(X47),X49),hAPP(X48,X47,X50,X52)))
        | ~ hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less_eq(X47),X49),hAPP(X48,X47,X50,X51)))
        | ~ hBOOL(hAPP(X48,bool,hAPP(X48,fun(X48,bool),ord_less(X48),X51),X52))
        | ~ order(X48)
        | ~ order(X47) )
      & ( ~ hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less(X47),hAPP(X48,X47,X50,esk55_6(X47,X48,X49,X50,X51,X52))),hAPP(X48,X47,X50,esk54_6(X47,X48,X49,X50,X51,X52))))
        | hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less(X47),X49),hAPP(X48,X47,X50,X52)))
        | ~ hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less_eq(X47),X49),hAPP(X48,X47,X50,X51)))
        | ~ hBOOL(hAPP(X48,bool,hAPP(X48,fun(X48,bool),ord_less(X48),X51),X52))
        | ~ order(X48)
        | ~ order(X47) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_628])])])])]) ).

fof(c_0_1237,plain,
    ! [X47,X48,X49,X50,X51,X52] :
      ( ( hBOOL(hAPP(X48,bool,hAPP(X48,fun(X48,bool),ord_less_eq(X48),esk46_6(X47,X48,X49,X50,X51,X52)),esk47_6(X47,X48,X49,X50,X51,X52)))
        | hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less(X47),X50),hAPP(X48,X47,X51,X49)))
        | ~ hBOOL(hAPP(X48,bool,hAPP(X48,fun(X48,bool),ord_less_eq(X48),X52),X49))
        | ~ hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less(X47),X50),hAPP(X48,X47,X51,X52)))
        | ~ order(X48)
        | ~ order(X47) )
      & ( ~ hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less_eq(X47),hAPP(X48,X47,X51,esk46_6(X47,X48,X49,X50,X51,X52))),hAPP(X48,X47,X51,esk47_6(X47,X48,X49,X50,X51,X52))))
        | hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less(X47),X50),hAPP(X48,X47,X51,X49)))
        | ~ hBOOL(hAPP(X48,bool,hAPP(X48,fun(X48,bool),ord_less_eq(X48),X52),X49))
        | ~ hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less(X47),X50),hAPP(X48,X47,X51,X52)))
        | ~ order(X48)
        | ~ order(X47) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_629])])])])]) ).

fof(c_0_1238,plain,
    ! [X47,X48,X49,X50,X51,X52] :
      ( ( hBOOL(hAPP(X48,bool,hAPP(X48,fun(X48,bool),ord_less(X48),esk44_6(X47,X48,X49,X50,X51,X52)),esk45_6(X47,X48,X49,X50,X51,X52)))
        | hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less(X47),X50),hAPP(X48,X47,X51,X49)))
        | ~ hBOOL(hAPP(X48,bool,hAPP(X48,fun(X48,bool),ord_less(X48),X52),X49))
        | ~ hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less_eq(X47),X50),hAPP(X48,X47,X51,X52)))
        | ~ order(X48)
        | ~ order(X47) )
      & ( ~ hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less(X47),hAPP(X48,X47,X51,esk44_6(X47,X48,X49,X50,X51,X52))),hAPP(X48,X47,X51,esk45_6(X47,X48,X49,X50,X51,X52))))
        | hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less(X47),X50),hAPP(X48,X47,X51,X49)))
        | ~ hBOOL(hAPP(X48,bool,hAPP(X48,fun(X48,bool),ord_less(X48),X52),X49))
        | ~ hBOOL(hAPP(X47,bool,hAPP(X47,fun(X47,bool),ord_less_eq(X47),X50),hAPP(X48,X47,X51,X52)))
        | ~ order(X48)
        | ~ order(X47) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_630])])])])]) ).

fof(c_0_1239,plain,
    ! [X17,X18,X19,X20,X21,X22] :
      ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X21),X22)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X18,esk2_6(X17,X18,X19,X20,X21,X22))))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X19),X20)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X17,esk2_6(X17,X18,X19,X20,X21,X22))))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X21),X22)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X18)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X19),X20)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X17)))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X17),arrow_1111136790e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X18),arrow_1111136790e_Prof))
        | ti(arrow_490897120le_alt,X22) = ti(arrow_490897120le_alt,X19)
        | ti(arrow_490897120le_alt,X21) = ti(arrow_490897120le_alt,X20)
        | ti(arrow_490897120le_alt,X19) = ti(arrow_490897120le_alt,X20)
        | ti(arrow_490897120le_alt,X21) = ti(arrow_490897120le_alt,X22) )
      & ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X21),X22)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X18,esk2_6(X17,X18,X19,X20,X21,X22))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X19),X20)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X17,esk2_6(X17,X18,X19,X20,X21,X22))))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X21),X22)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X18)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X19),X20)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X17)))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X17),arrow_1111136790e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X18),arrow_1111136790e_Prof))
        | ti(arrow_490897120le_alt,X22) = ti(arrow_490897120le_alt,X19)
        | ti(arrow_490897120le_alt,X21) = ti(arrow_490897120le_alt,X20)
        | ti(arrow_490897120le_alt,X19) = ti(arrow_490897120le_alt,X20)
        | ti(arrow_490897120le_alt,X21) = ti(arrow_490897120le_alt,X22) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_631])])])]) ).

fof(c_0_1240,plain,
    ! [X17,X18,X19,X20,X21,X22] :
      ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X21),X22)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X18)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X19),X20)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X17)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X21),X22)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X18,esk1_6(X17,X18,X19,X20,X21,X22))))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X19),X20)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X17,esk1_6(X17,X18,X19,X20,X21,X22))))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X17),arrow_1111136790e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X18),arrow_1111136790e_Prof))
        | ti(arrow_490897120le_alt,X22) = ti(arrow_490897120le_alt,X19)
        | ti(arrow_490897120le_alt,X21) = ti(arrow_490897120le_alt,X20)
        | ti(arrow_490897120le_alt,X19) = ti(arrow_490897120le_alt,X20)
        | ti(arrow_490897120le_alt,X21) = ti(arrow_490897120le_alt,X22) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X19),X20)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X17)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X21),X22)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X18)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X21),X22)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X18,esk1_6(X17,X18,X19,X20,X21,X22))))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X19),X20)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X17,esk1_6(X17,X18,X19,X20,X21,X22))))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X17),arrow_1111136790e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X18),arrow_1111136790e_Prof))
        | ti(arrow_490897120le_alt,X22) = ti(arrow_490897120le_alt,X19)
        | ti(arrow_490897120le_alt,X21) = ti(arrow_490897120le_alt,X20)
        | ti(arrow_490897120le_alt,X19) = ti(arrow_490897120le_alt,X20)
        | ti(arrow_490897120le_alt,X21) = ti(arrow_490897120le_alt,X22) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X21),X22)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X18)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X19),X20)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X17)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X21),X22)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X18,esk1_6(X17,X18,X19,X20,X21,X22))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X19),X20)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X17,esk1_6(X17,X18,X19,X20,X21,X22))))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X17),arrow_1111136790e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X18),arrow_1111136790e_Prof))
        | ti(arrow_490897120le_alt,X22) = ti(arrow_490897120le_alt,X19)
        | ti(arrow_490897120le_alt,X21) = ti(arrow_490897120le_alt,X20)
        | ti(arrow_490897120le_alt,X19) = ti(arrow_490897120le_alt,X20)
        | ti(arrow_490897120le_alt,X21) = ti(arrow_490897120le_alt,X22) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X19),X20)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X17)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X21),X22)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X18)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X21),X22)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X18,esk1_6(X17,X18,X19,X20,X21,X22))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X19),X20)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X17,esk1_6(X17,X18,X19,X20,X21,X22))))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X17),arrow_1111136790e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X18),arrow_1111136790e_Prof))
        | ti(arrow_490897120le_alt,X22) = ti(arrow_490897120le_alt,X19)
        | ti(arrow_490897120le_alt,X21) = ti(arrow_490897120le_alt,X20)
        | ti(arrow_490897120le_alt,X19) = ti(arrow_490897120le_alt,X20)
        | ti(arrow_490897120le_alt,X21) = ti(arrow_490897120le_alt,X22) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_632])])])]) ).

fof(c_0_1241,plain,
    ! [X17,X18,X19,X20,X21,X22] :
      ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X21),X22)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X18)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X19),X20)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X17)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X21),X22)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X18,esk4_6(X17,X18,X19,X20,X21,X22))))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X19),X20)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X17,esk4_6(X17,X18,X19,X20,X21,X22))))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X17),arrow_1111136790e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X18),arrow_1111136790e_Prof))
        | ti(arrow_490897120le_alt,X19) = ti(arrow_490897120le_alt,X20)
        | ti(arrow_490897120le_alt,X21) = ti(arrow_490897120le_alt,X22) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X19),X20)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X17)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X21),X22)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X18)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X21),X22)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X18,esk4_6(X17,X18,X19,X20,X21,X22))))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X19),X20)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X17,esk4_6(X17,X18,X19,X20,X21,X22))))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X17),arrow_1111136790e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X18),arrow_1111136790e_Prof))
        | ti(arrow_490897120le_alt,X19) = ti(arrow_490897120le_alt,X20)
        | ti(arrow_490897120le_alt,X21) = ti(arrow_490897120le_alt,X22) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X21),X22)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X18)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X19),X20)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X17)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X21),X22)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X18,esk4_6(X17,X18,X19,X20,X21,X22))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X19),X20)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X17,esk4_6(X17,X18,X19,X20,X21,X22))))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X17),arrow_1111136790e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X18),arrow_1111136790e_Prof))
        | ti(arrow_490897120le_alt,X19) = ti(arrow_490897120le_alt,X20)
        | ti(arrow_490897120le_alt,X21) = ti(arrow_490897120le_alt,X22) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X19),X20)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X17)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X21),X22)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X18)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X21),X22)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X18,esk4_6(X17,X18,X19,X20,X21,X22))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X19),X20)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X17,esk4_6(X17,X18,X19,X20,X21,X22))))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X17),arrow_1111136790e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X18),arrow_1111136790e_Prof))
        | ti(arrow_490897120le_alt,X19) = ti(arrow_490897120le_alt,X20)
        | ti(arrow_490897120le_alt,X21) = ti(arrow_490897120le_alt,X22) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_633])])])]) ).

fof(c_0_1242,plain,
    ! [X72,X73] :
      ( ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),X73))
      | hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),X73))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,X72))))) != zero_zero(nat) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_634])]) ).

fof(c_0_1243,plain,
    ! [X17,X18] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),n))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),n)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),n))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),n)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
        | hAPP(arrow_660593299e_indi,nat,h,X17) != n
        | hAPP(arrow_660593299e_indi,nat,h,X17) = n
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),n)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
        | hAPP(arrow_660593299e_indi,nat,h,X17) != n
        | hAPP(arrow_660593299e_indi,nat,h,X17) = n
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),n)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X17)),e)))
        | hAPP(arrow_660593299e_indi,nat,h,X17) = n
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),n)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X17)),e)))
        | hAPP(arrow_660593299e_indi,nat,h,X17) = n
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),n)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
        | hAPP(arrow_660593299e_indi,nat,h,X17) != n
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X17)),c),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),n)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
        | hAPP(arrow_660593299e_indi,nat,h,X17) != n
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X17)),c),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),n)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X17)),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X17)),c),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),n)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X17)),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X17)),c),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),n)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),n))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X17)),e))) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),n))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X17)),e))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
        | hAPP(arrow_660593299e_indi,nat,h,X17) != n
        | hAPP(arrow_660593299e_indi,nat,h,X17) = n
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X17)),e))) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
        | hAPP(arrow_660593299e_indi,nat,h,X17) != n
        | hAPP(arrow_660593299e_indi,nat,h,X17) = n
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X17)),e))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X17)),e)))
        | hAPP(arrow_660593299e_indi,nat,h,X17) = n
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X17)),e))) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X17)),e)))
        | hAPP(arrow_660593299e_indi,nat,h,X17) = n
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X17)),e))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
        | hAPP(arrow_660593299e_indi,nat,h,X17) != n
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X17)),c),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X17)),e))) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
        | hAPP(arrow_660593299e_indi,nat,h,X17) != n
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X17)),c),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X17)),e))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X17)),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X17)),c),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X17)),e))) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X17)),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X17)),c),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X17)),e))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X18)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X18)),e)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X18)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X18)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) )
      & ( hAPP(arrow_660593299e_indi,nat,h,X18) != n
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X18)),c),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X18)),n))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X18)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X18)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) )
      & ( hAPP(arrow_660593299e_indi,nat,h,X18) = n
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X18)),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X18)),n))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X18)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X18)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X18)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X18)),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X18)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) )
      & ( hAPP(arrow_660593299e_indi,nat,h,X18) != n
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X18)),c),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X18)),n))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X18)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) )
      & ( hAPP(arrow_660593299e_indi,nat,h,X18) = n
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X18)),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X18)),n))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X18)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X18)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X18)),e)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X18)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab)) )
      & ( hAPP(arrow_660593299e_indi,nat,h,X18) != n
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X18)),c),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X18)),n))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X18)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab)) )
      & ( hAPP(arrow_660593299e_indi,nat,h,X18) = n
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X18)),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X18)),n))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X18)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X18)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X18)),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab)) )
      & ( hAPP(arrow_660593299e_indi,nat,h,X18) != n
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X18)),c),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X18)),n))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab)) )
      & ( hAPP(arrow_660593299e_indi,nat,h,X18) = n
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X18)),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X18)),n))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_635])])])])]) ).

fof(c_0_1244,plain,
    ! [X43,X44] :
      ( ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),esk23_2(X43,X44)),arrow_1111136790e_Prof))
        | hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,X44),X43))
        | ~ hBOOL(hAPP(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X44),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1111136790e_Prof),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_2064824852le_Lin)))) )
      & ( ti(arrow_490897120le_alt,esk24_2(X43,X44)) != ti(arrow_490897120le_alt,esk25_2(X43,X44))
        | hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,X44),X43))
        | ~ hBOOL(hAPP(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X44),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1111136790e_Prof),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_2064824852le_Lin)))) )
      & ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),esk24_2(X43,X44)),esk25_2(X43,X44))),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),esk23_2(X43,X44),X43)))
        | hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,X44),X43))
        | ~ hBOOL(hAPP(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X44),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1111136790e_Prof),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_2064824852le_Lin)))) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),esk24_2(X43,X44)),esk25_2(X43,X44))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X44,esk23_2(X43,X44))))
        | hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,X44),X43))
        | ~ hBOOL(hAPP(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X44),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1111136790e_Prof),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_2064824852le_Lin)))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_636])])])]) ).

fof(c_0_1245,plain,
    ! [X17,X18] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),n))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),n)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),n))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),n)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
        | hAPP(arrow_660593299e_indi,nat,h,X17) != n
        | hAPP(arrow_660593299e_indi,nat,h,X17) = n
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),n)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
        | hAPP(arrow_660593299e_indi,nat,h,X17) != n
        | hAPP(arrow_660593299e_indi,nat,h,X17) = n
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),n)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X17)),e)))
        | hAPP(arrow_660593299e_indi,nat,h,X17) = n
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),n)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X17)),e)))
        | hAPP(arrow_660593299e_indi,nat,h,X17) = n
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),n)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
        | hAPP(arrow_660593299e_indi,nat,h,X17) != n
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X17)),c),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),n)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
        | hAPP(arrow_660593299e_indi,nat,h,X17) != n
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X17)),c),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),n)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X17)),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X17)),c),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),n)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X17)),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X17)),c),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),n)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),n))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X17)),e))) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),n))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X17)),e))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
        | hAPP(arrow_660593299e_indi,nat,h,X17) != n
        | hAPP(arrow_660593299e_indi,nat,h,X17) = n
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X17)),e))) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
        | hAPP(arrow_660593299e_indi,nat,h,X17) != n
        | hAPP(arrow_660593299e_indi,nat,h,X17) = n
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X17)),e))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X17)),e)))
        | hAPP(arrow_660593299e_indi,nat,h,X17) = n
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X17)),e))) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X17)),e)))
        | hAPP(arrow_660593299e_indi,nat,h,X17) = n
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X17)),e))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
        | hAPP(arrow_660593299e_indi,nat,h,X17) != n
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X17)),c),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X17)),e))) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
        | hAPP(arrow_660593299e_indi,nat,h,X17) != n
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X17)),c),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X17)),e))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X17)),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X17)),c),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X17)),e))) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X17)),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X17)),c),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X17)),e))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X18)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X18)),e)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X18)),n))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X18)),n)) )
      & ( hAPP(arrow_660593299e_indi,nat,h,X18) != n
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X18)),c),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X18)),n))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X18)),n))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X18)),n)) )
      & ( hAPP(arrow_660593299e_indi,nat,h,X18) = n
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X18)),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X18)),n))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X18)),n))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X18)),n)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X18)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X18)),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X18)),n)) )
      & ( hAPP(arrow_660593299e_indi,nat,h,X18) != n
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X18)),c),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X18)),n))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X18)),n)) )
      & ( hAPP(arrow_660593299e_indi,nat,h,X18) = n
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X18)),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X18)),n))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X18)),n)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X18)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X18)),e)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X18)),n))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab)) )
      & ( hAPP(arrow_660593299e_indi,nat,h,X18) != n
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X18)),c),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X18)),n))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X18)),n))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab)) )
      & ( hAPP(arrow_660593299e_indi,nat,h,X18) = n
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X18)),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X18)),n))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X18)),n))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X18)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X18)),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab)) )
      & ( hAPP(arrow_660593299e_indi,nat,h,X18) != n
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X18)),c),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X18)),n))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab)) )
      & ( hAPP(arrow_660593299e_indi,nat,h,X18) = n
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X18)),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X18)),n))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_637])])])])]) ).

fof(c_0_1246,plain,
    ! [X17,X18] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X17)),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X17))) )
      & ( hAPP(arrow_660593299e_indi,nat,h,X17) != n
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X17)),c),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),n))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X17))) )
      & ( hAPP(arrow_660593299e_indi,nat,h,X17) = n
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X17)),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X17)),n))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X17))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X18)),n))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X18)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X18))) )
      & ( hAPP(arrow_660593299e_indi,nat,h,X18) != n
        | hAPP(arrow_660593299e_indi,nat,h,X18) = n
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X18)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X18))) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X18)),e)))
        | hAPP(arrow_660593299e_indi,nat,h,X18) = n
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X18)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X18))) )
      & ( hAPP(arrow_660593299e_indi,nat,h,X18) != n
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X18)),c),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X18)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X18))) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X18)),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X18)),c),e)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X18)),n))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X18))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X18)),n))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X18)),e)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X18))) )
      & ( hAPP(arrow_660593299e_indi,nat,h,X18) != n
        | hAPP(arrow_660593299e_indi,nat,h,X18) = n
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X18)),e)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X18))) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X18)),e)))
        | hAPP(arrow_660593299e_indi,nat,h,X18) = n
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X18)),e)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X18))) )
      & ( hAPP(arrow_660593299e_indi,nat,h,X18) != n
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X18)),c),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X18)),e)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X18))) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X18)),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X18)),c),e)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X18)),e)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X18))) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_638])])])])]) ).

fof(c_0_1247,plain,
    ! [X28,X29,X30,X31,X32,X34,X39,X40] :
      ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X31),X32)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X28,X29)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X31),X32)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X28,X30)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X31),X32)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X29,esk9_5(X28,X29,X30,X31,X32))))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X31),X32)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X30,esk9_5(X28,X29,X30,X31,X32))))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X30),arrow_1111136790e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X29),arrow_1111136790e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X28)) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X31),X32)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X28,X30)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X31),X32)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X28,X29)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X31),X32)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X29,esk9_5(X28,X29,X30,X31,X32))))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X31),X32)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X30,esk9_5(X28,X29,X30,X31,X32))))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X30),arrow_1111136790e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X29),arrow_1111136790e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X28)) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X31),X32)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X28,X29)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X31),X32)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X28,X30)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X31),X32)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X29,esk9_5(X28,X29,X30,X31,X32))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X31),X32)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X30,esk9_5(X28,X29,X30,X31,X32))))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X30),arrow_1111136790e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X29),arrow_1111136790e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X28)) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X31),X32)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X28,X30)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X31),X32)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X28,X29)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X31),X32)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X29,esk9_5(X28,X29,X30,X31,X32))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X31),X32)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X30,esk9_5(X28,X29,X30,X31,X32))))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X30),arrow_1111136790e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X29),arrow_1111136790e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X28)) )
      & ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),esk10_1(X34)),arrow_1111136790e_Prof))
        | hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X34)) )
      & ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),esk11_1(X34)),arrow_1111136790e_Prof))
        | hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X34)) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),esk12_1(X34)),esk13_1(X34))),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),esk10_1(X34),X39)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),esk12_1(X34)),esk13_1(X34))),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),esk11_1(X34),X39)))
        | hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X34)) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),esk12_1(X34)),esk13_1(X34))),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),esk11_1(X34),X40)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),esk12_1(X34)),esk13_1(X34))),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),esk10_1(X34),X40)))
        | hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X34)) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),esk12_1(X34)),esk13_1(X34))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X34,esk10_1(X34))))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),esk12_1(X34)),esk13_1(X34))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X34,esk11_1(X34))))
        | hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X34)) )
      & ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),esk12_1(X34)),esk13_1(X34))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X34,esk10_1(X34))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),esk12_1(X34)),esk13_1(X34))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X34,esk11_1(X34))))
        | hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X34)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_639])])])])])]) ).

fof(c_0_1248,plain,
    ! [X18,X19,X20,X21,X22] :
      ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X21),X22)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X19)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X22),X20)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X18)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X21),X22)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X19,esk3_5(X18,X19,X20,X21,X22))))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X22),X20)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X18,esk3_5(X18,X19,X20,X21,X22))))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X18),arrow_1111136790e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X19),arrow_1111136790e_Prof))
        | ti(arrow_490897120le_alt,X21) = ti(arrow_490897120le_alt,X20)
        | ti(arrow_490897120le_alt,X22) = ti(arrow_490897120le_alt,X20)
        | ti(arrow_490897120le_alt,X21) = ti(arrow_490897120le_alt,X22) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X22),X20)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X18)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X21),X22)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X19)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X21),X22)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X19,esk3_5(X18,X19,X20,X21,X22))))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X22),X20)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X18,esk3_5(X18,X19,X20,X21,X22))))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X18),arrow_1111136790e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X19),arrow_1111136790e_Prof))
        | ti(arrow_490897120le_alt,X21) = ti(arrow_490897120le_alt,X20)
        | ti(arrow_490897120le_alt,X22) = ti(arrow_490897120le_alt,X20)
        | ti(arrow_490897120le_alt,X21) = ti(arrow_490897120le_alt,X22) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X21),X22)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X19)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X22),X20)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X18)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X21),X22)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X19,esk3_5(X18,X19,X20,X21,X22))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X22),X20)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X18,esk3_5(X18,X19,X20,X21,X22))))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X18),arrow_1111136790e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X19),arrow_1111136790e_Prof))
        | ti(arrow_490897120le_alt,X21) = ti(arrow_490897120le_alt,X20)
        | ti(arrow_490897120le_alt,X22) = ti(arrow_490897120le_alt,X20)
        | ti(arrow_490897120le_alt,X21) = ti(arrow_490897120le_alt,X22) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X22),X20)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X18)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X21),X22)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X19)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X21),X22)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X19,esk3_5(X18,X19,X20,X21,X22))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X22),X20)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X18,esk3_5(X18,X19,X20,X21,X22))))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X18),arrow_1111136790e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X19),arrow_1111136790e_Prof))
        | ti(arrow_490897120le_alt,X21) = ti(arrow_490897120le_alt,X20)
        | ti(arrow_490897120le_alt,X22) = ti(arrow_490897120le_alt,X20)
        | ti(arrow_490897120le_alt,X21) = ti(arrow_490897120le_alt,X22) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_640])])])]) ).

fof(c_0_1249,plain,
    ! [X51,X52,X53,X54,X55,X56] :
      ( ( hBOOL(hAPP(fun(X51,bool),bool,finite_finite_1(X51),hAPP(fun(X51,bool),fun(X51,bool),collect(X51),X52)))
        | ~ hBOOL(hAPP(fun(X51,bool),bool,finite_finite_1(X51),hAPP(fun(X51,bool),fun(X51,bool),collect(X51),hAPP(fun(X51,bool),fun(X51,bool),hAPP(fun(X51,fun(bool,bool)),fun(fun(X51,bool),fun(X51,bool)),combs(X51,bool,bool),hAPP(fun(X51,bool),fun(X51,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X51,bool),fun(X51,fun(bool,bool))),combb(bool,fun(bool,bool),X51),fdisj),X52)),X53)))) )
      & ( hBOOL(hAPP(fun(X51,bool),bool,finite_finite_1(X51),hAPP(fun(X51,bool),fun(X51,bool),collect(X51),X53)))
        | ~ hBOOL(hAPP(fun(X51,bool),bool,finite_finite_1(X51),hAPP(fun(X51,bool),fun(X51,bool),collect(X51),hAPP(fun(X51,bool),fun(X51,bool),hAPP(fun(X51,fun(bool,bool)),fun(fun(X51,bool),fun(X51,bool)),combs(X51,bool,bool),hAPP(fun(X51,bool),fun(X51,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X51,bool),fun(X51,fun(bool,bool))),combb(bool,fun(bool,bool),X51),fdisj),X52)),X53)))) )
      & ( ~ hBOOL(hAPP(fun(X54,bool),bool,finite_finite_1(X54),hAPP(fun(X54,bool),fun(X54,bool),collect(X54),X55)))
        | ~ hBOOL(hAPP(fun(X54,bool),bool,finite_finite_1(X54),hAPP(fun(X54,bool),fun(X54,bool),collect(X54),X56)))
        | hBOOL(hAPP(fun(X54,bool),bool,finite_finite_1(X54),hAPP(fun(X54,bool),fun(X54,bool),collect(X54),hAPP(fun(X54,bool),fun(X54,bool),hAPP(fun(X54,fun(bool,bool)),fun(fun(X54,bool),fun(X54,bool)),combs(X54,bool,bool),hAPP(fun(X54,bool),fun(X54,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X54,bool),fun(X54,fun(bool,bool))),combb(bool,fun(bool,bool),X54),fdisj),X55)),X56)))) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_641])])])])]) ).

fof(c_0_1250,plain,
    ! [X17,X18,X19,X20] :
      ( ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X19),X20)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X18)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X20),X19)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X17)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X19),X20)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X18,esk5_4(X17,X18,X19,X20))))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X20),X19)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X17,esk5_4(X17,X18,X19,X20))))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X17),arrow_1111136790e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X18),arrow_1111136790e_Prof))
        | ti(arrow_490897120le_alt,X19) = ti(arrow_490897120le_alt,X20) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X20),X19)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X17)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X19),X20)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X18)))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X19),X20)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X18,esk5_4(X17,X18,X19,X20))))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X20),X19)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X17,esk5_4(X17,X18,X19,X20))))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X17),arrow_1111136790e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X18),arrow_1111136790e_Prof))
        | ti(arrow_490897120le_alt,X19) = ti(arrow_490897120le_alt,X20) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X19),X20)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X18)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X20),X19)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X17)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X19),X20)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X18,esk5_4(X17,X18,X19,X20))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X20),X19)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X17,esk5_4(X17,X18,X19,X20))))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X17),arrow_1111136790e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X18),arrow_1111136790e_Prof))
        | ti(arrow_490897120le_alt,X19) = ti(arrow_490897120le_alt,X20) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X20),X19)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X17)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X19),X20)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X18)))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X19),X20)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X18,esk5_4(X17,X18,X19,X20))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X20),X19)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X17,esk5_4(X17,X18,X19,X20))))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X17),arrow_1111136790e_Prof))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X18),arrow_1111136790e_Prof))
        | ti(arrow_490897120le_alt,X19) = ti(arrow_490897120le_alt,X20) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_642])])])]) ).

fof(c_0_1251,plain,
    ! [X43,X44] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),X43)),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X44))))),
    inference(variable_rename,[status(thm)],[c_0_643]) ).

fof(c_0_1252,plain,
    ! [X16,X17,X18,X19,X20] :
      ( ( ti(arrow_490897120le_alt,X16) != ti(arrow_490897120le_alt,X17)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X17)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X18),X19),X20)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X18),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X19) = ti(arrow_490897120le_alt,X20) )
      & ( ti(arrow_490897120le_alt,X17) != ti(arrow_490897120le_alt,X19)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X20)),X18))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X17)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X18),X19),X20)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X18),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X19) = ti(arrow_490897120le_alt,X20) )
      & ( ti(arrow_490897120le_alt,X16) != ti(arrow_490897120le_alt,X19)
        | ti(arrow_490897120le_alt,X17) = ti(arrow_490897120le_alt,X20)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X20),X17)),X18))
        | ti(arrow_490897120le_alt,X17) = ti(arrow_490897120le_alt,X19)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X17)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X18),X19),X20)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X18),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X19) = ti(arrow_490897120le_alt,X20) )
      & ( ti(arrow_490897120le_alt,X16) = ti(arrow_490897120le_alt,X19)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X17)),X18))
        | ti(arrow_490897120le_alt,X17) = ti(arrow_490897120le_alt,X19)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X17)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X18),X19),X20)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X18),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X19) = ti(arrow_490897120le_alt,X20) )
      & ( ti(arrow_490897120le_alt,X17) != ti(arrow_490897120le_alt,X19)
        | ti(arrow_490897120le_alt,X17) = ti(arrow_490897120le_alt,X19)
        | ti(arrow_490897120le_alt,X16) = ti(arrow_490897120le_alt,X17)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X17)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X18),X19),X20)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X18),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X19) = ti(arrow_490897120le_alt,X20) )
      & ( ti(arrow_490897120le_alt,X16) != ti(arrow_490897120le_alt,X19)
        | ti(arrow_490897120le_alt,X16) = ti(arrow_490897120le_alt,X19)
        | ti(arrow_490897120le_alt,X17) = ti(arrow_490897120le_alt,X19)
        | ti(arrow_490897120le_alt,X16) = ti(arrow_490897120le_alt,X17)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X17)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X18),X19),X20)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X18),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X19) = ti(arrow_490897120le_alt,X20) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X17)),X18))
        | ti(arrow_490897120le_alt,X16) = ti(arrow_490897120le_alt,X19)
        | ti(arrow_490897120le_alt,X17) = ti(arrow_490897120le_alt,X19)
        | ti(arrow_490897120le_alt,X16) = ti(arrow_490897120le_alt,X17)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X17)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X18),X19),X20)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X18),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X19) = ti(arrow_490897120le_alt,X20) )
      & ( ti(arrow_490897120le_alt,X16) != ti(arrow_490897120le_alt,X19)
        | ti(arrow_490897120le_alt,X17) != ti(arrow_490897120le_alt,X20)
        | ti(arrow_490897120le_alt,X17) = ti(arrow_490897120le_alt,X19)
        | ti(arrow_490897120le_alt,X16) = ti(arrow_490897120le_alt,X17)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X17)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X18),X19),X20)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X18),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X19) = ti(arrow_490897120le_alt,X20) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X17)),X18))
        | ti(arrow_490897120le_alt,X17) != ti(arrow_490897120le_alt,X20)
        | ti(arrow_490897120le_alt,X17) = ti(arrow_490897120le_alt,X19)
        | ti(arrow_490897120le_alt,X16) = ti(arrow_490897120le_alt,X17)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X17)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X18),X19),X20)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X18),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X19) = ti(arrow_490897120le_alt,X20) )
      & ( ti(arrow_490897120le_alt,X16) != ti(arrow_490897120le_alt,X19)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X20),X17)),X18))
        | ti(arrow_490897120le_alt,X17) = ti(arrow_490897120le_alt,X19)
        | ti(arrow_490897120le_alt,X16) = ti(arrow_490897120le_alt,X17)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X17)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X18),X19),X20)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X18),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X19) = ti(arrow_490897120le_alt,X20) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X17)),X18))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X20),X17)),X18))
        | ti(arrow_490897120le_alt,X17) = ti(arrow_490897120le_alt,X19)
        | ti(arrow_490897120le_alt,X16) = ti(arrow_490897120le_alt,X17)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X17)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X18),X19),X20)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X18),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X19) = ti(arrow_490897120le_alt,X20) )
      & ( ti(arrow_490897120le_alt,X17) != ti(arrow_490897120le_alt,X19)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X20)),X18))
        | ti(arrow_490897120le_alt,X16) = ti(arrow_490897120le_alt,X17)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X17)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X18),X19),X20)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X18),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X19) = ti(arrow_490897120le_alt,X20) )
      & ( ti(arrow_490897120le_alt,X16) != ti(arrow_490897120le_alt,X19)
        | ti(arrow_490897120le_alt,X16) = ti(arrow_490897120le_alt,X19)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X20)),X18))
        | ti(arrow_490897120le_alt,X16) = ti(arrow_490897120le_alt,X17)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X17)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X18),X19),X20)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X18),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X19) = ti(arrow_490897120le_alt,X20) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X17)),X18))
        | ti(arrow_490897120le_alt,X16) = ti(arrow_490897120le_alt,X19)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X20)),X18))
        | ti(arrow_490897120le_alt,X16) = ti(arrow_490897120le_alt,X17)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X17)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X18),X19),X20)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X18),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X19) = ti(arrow_490897120le_alt,X20) )
      & ( ti(arrow_490897120le_alt,X16) != ti(arrow_490897120le_alt,X19)
        | ti(arrow_490897120le_alt,X17) != ti(arrow_490897120le_alt,X20)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X20)),X18))
        | ti(arrow_490897120le_alt,X16) = ti(arrow_490897120le_alt,X17)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X17)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X18),X19),X20)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X18),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X19) = ti(arrow_490897120le_alt,X20) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X17)),X18))
        | ti(arrow_490897120le_alt,X17) != ti(arrow_490897120le_alt,X20)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X20)),X18))
        | ti(arrow_490897120le_alt,X16) = ti(arrow_490897120le_alt,X17)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X17)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X18),X19),X20)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X18),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X19) = ti(arrow_490897120le_alt,X20) )
      & ( ti(arrow_490897120le_alt,X16) != ti(arrow_490897120le_alt,X19)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X20),X17)),X18))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X20)),X18))
        | ti(arrow_490897120le_alt,X16) = ti(arrow_490897120le_alt,X17)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X17)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X18),X19),X20)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X18),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X19) = ti(arrow_490897120le_alt,X20) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X17)),X18))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X20),X17)),X18))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X20)),X18))
        | ti(arrow_490897120le_alt,X16) = ti(arrow_490897120le_alt,X17)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X17)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X18),X19),X20)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X18),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X19) = ti(arrow_490897120le_alt,X20) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_644])])]) ).

fof(c_0_1253,plain,
    ! [X16,X17,X18,X19,X20] :
      ( ( ti(arrow_490897120le_alt,X16) != ti(arrow_490897120le_alt,X17)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X17)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X18),X19),X20)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X18),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X19) = ti(arrow_490897120le_alt,X20) )
      & ( ti(arrow_490897120le_alt,X16) != ti(arrow_490897120le_alt,X20)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X19),X17)),X18))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X17)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X18),X19),X20)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X18),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X19) = ti(arrow_490897120le_alt,X20) )
      & ( ti(arrow_490897120le_alt,X17) != ti(arrow_490897120le_alt,X20)
        | ti(arrow_490897120le_alt,X16) = ti(arrow_490897120le_alt,X19)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X19)),X18))
        | ti(arrow_490897120le_alt,X16) = ti(arrow_490897120le_alt,X20)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X17)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X18),X19),X20)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X18),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X19) = ti(arrow_490897120le_alt,X20) )
      & ( ti(arrow_490897120le_alt,X17) = ti(arrow_490897120le_alt,X20)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X17)),X18))
        | ti(arrow_490897120le_alt,X16) = ti(arrow_490897120le_alt,X20)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X17)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X18),X19),X20)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X18),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X19) = ti(arrow_490897120le_alt,X20) )
      & ( ti(arrow_490897120le_alt,X16) != ti(arrow_490897120le_alt,X20)
        | ti(arrow_490897120le_alt,X16) = ti(arrow_490897120le_alt,X20)
        | ti(arrow_490897120le_alt,X16) = ti(arrow_490897120le_alt,X17)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X17)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X18),X19),X20)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X18),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X19) = ti(arrow_490897120le_alt,X20) )
      & ( ti(arrow_490897120le_alt,X17) != ti(arrow_490897120le_alt,X20)
        | ti(arrow_490897120le_alt,X17) = ti(arrow_490897120le_alt,X20)
        | ti(arrow_490897120le_alt,X16) = ti(arrow_490897120le_alt,X20)
        | ti(arrow_490897120le_alt,X16) = ti(arrow_490897120le_alt,X17)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X17)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X18),X19),X20)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X18),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X19) = ti(arrow_490897120le_alt,X20) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X17)),X18))
        | ti(arrow_490897120le_alt,X17) = ti(arrow_490897120le_alt,X20)
        | ti(arrow_490897120le_alt,X16) = ti(arrow_490897120le_alt,X20)
        | ti(arrow_490897120le_alt,X16) = ti(arrow_490897120le_alt,X17)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X17)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X18),X19),X20)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X18),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X19) = ti(arrow_490897120le_alt,X20) )
      & ( ti(arrow_490897120le_alt,X17) != ti(arrow_490897120le_alt,X20)
        | ti(arrow_490897120le_alt,X16) != ti(arrow_490897120le_alt,X19)
        | ti(arrow_490897120le_alt,X16) = ti(arrow_490897120le_alt,X20)
        | ti(arrow_490897120le_alt,X16) = ti(arrow_490897120le_alt,X17)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X17)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X18),X19),X20)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X18),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X19) = ti(arrow_490897120le_alt,X20) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X17)),X18))
        | ti(arrow_490897120le_alt,X16) != ti(arrow_490897120le_alt,X19)
        | ti(arrow_490897120le_alt,X16) = ti(arrow_490897120le_alt,X20)
        | ti(arrow_490897120le_alt,X16) = ti(arrow_490897120le_alt,X17)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X17)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X18),X19),X20)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X18),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X19) = ti(arrow_490897120le_alt,X20) )
      & ( ti(arrow_490897120le_alt,X17) != ti(arrow_490897120le_alt,X20)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X19)),X18))
        | ti(arrow_490897120le_alt,X16) = ti(arrow_490897120le_alt,X20)
        | ti(arrow_490897120le_alt,X16) = ti(arrow_490897120le_alt,X17)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X17)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X18),X19),X20)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X18),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X19) = ti(arrow_490897120le_alt,X20) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X17)),X18))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X19)),X18))
        | ti(arrow_490897120le_alt,X16) = ti(arrow_490897120le_alt,X20)
        | ti(arrow_490897120le_alt,X16) = ti(arrow_490897120le_alt,X17)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X17)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X18),X19),X20)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X18),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X19) = ti(arrow_490897120le_alt,X20) )
      & ( ti(arrow_490897120le_alt,X16) != ti(arrow_490897120le_alt,X20)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X19),X17)),X18))
        | ti(arrow_490897120le_alt,X16) = ti(arrow_490897120le_alt,X17)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X17)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X18),X19),X20)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X18),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X19) = ti(arrow_490897120le_alt,X20) )
      & ( ti(arrow_490897120le_alt,X17) != ti(arrow_490897120le_alt,X20)
        | ti(arrow_490897120le_alt,X17) = ti(arrow_490897120le_alt,X20)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X19),X17)),X18))
        | ti(arrow_490897120le_alt,X16) = ti(arrow_490897120le_alt,X17)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X17)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X18),X19),X20)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X18),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X19) = ti(arrow_490897120le_alt,X20) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X17)),X18))
        | ti(arrow_490897120le_alt,X17) = ti(arrow_490897120le_alt,X20)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X19),X17)),X18))
        | ti(arrow_490897120le_alt,X16) = ti(arrow_490897120le_alt,X17)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X17)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X18),X19),X20)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X18),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X19) = ti(arrow_490897120le_alt,X20) )
      & ( ti(arrow_490897120le_alt,X17) != ti(arrow_490897120le_alt,X20)
        | ti(arrow_490897120le_alt,X16) != ti(arrow_490897120le_alt,X19)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X19),X17)),X18))
        | ti(arrow_490897120le_alt,X16) = ti(arrow_490897120le_alt,X17)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X17)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X18),X19),X20)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X18),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X19) = ti(arrow_490897120le_alt,X20) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X17)),X18))
        | ti(arrow_490897120le_alt,X16) != ti(arrow_490897120le_alt,X19)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X19),X17)),X18))
        | ti(arrow_490897120le_alt,X16) = ti(arrow_490897120le_alt,X17)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X17)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X18),X19),X20)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X18),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X19) = ti(arrow_490897120le_alt,X20) )
      & ( ti(arrow_490897120le_alt,X17) != ti(arrow_490897120le_alt,X20)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X19)),X18))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X19),X17)),X18))
        | ti(arrow_490897120le_alt,X16) = ti(arrow_490897120le_alt,X17)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X17)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X18),X19),X20)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X18),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X19) = ti(arrow_490897120le_alt,X20) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X17)),X18))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X19)),X18))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X19),X17)),X18))
        | ti(arrow_490897120le_alt,X16) = ti(arrow_490897120le_alt,X17)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X17)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X18),X19),X20)))
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X18),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X19) = ti(arrow_490897120le_alt,X20) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_645])])]) ).

fof(c_0_1254,plain,
    ! [X50,X51,X52,X53,X54] :
      ( ( hBOOL(hAPP(fun(X51,bool),bool,hAPP(X51,fun(fun(X51,bool),bool),member(X51),esk52_5(X50,X51,X52,X53,X54)),X54))
        | hBOOL(hAPP(fun(fun(X51,X50),bool),bool,hAPP(fun(fun(X51,X50),bool),fun(fun(fun(X51,X50),bool),bool),ord_less_eq(fun(fun(X51,X50),bool)),hAPP(fun(X51,fun(X50,bool)),fun(fun(X51,X50),bool),hAPP(fun(X51,bool),fun(fun(X51,fun(X50,bool)),fun(fun(X51,X50),bool)),pi(X51,X50),X54),X52)),hAPP(fun(X51,fun(X50,bool)),fun(fun(X51,X50),bool),hAPP(fun(X51,bool),fun(fun(X51,fun(X50,bool)),fun(fun(X51,X50),bool)),pi(X51,X50),X54),X53))) )
      & ( ~ hBOOL(hAPP(fun(X50,bool),bool,hAPP(fun(X50,bool),fun(fun(X50,bool),bool),ord_less_eq(fun(X50,bool)),hAPP(X51,fun(X50,bool),X52,esk52_5(X50,X51,X52,X53,X54))),hAPP(X51,fun(X50,bool),X53,esk52_5(X50,X51,X52,X53,X54))))
        | hBOOL(hAPP(fun(fun(X51,X50),bool),bool,hAPP(fun(fun(X51,X50),bool),fun(fun(fun(X51,X50),bool),bool),ord_less_eq(fun(fun(X51,X50),bool)),hAPP(fun(X51,fun(X50,bool)),fun(fun(X51,X50),bool),hAPP(fun(X51,bool),fun(fun(X51,fun(X50,bool)),fun(fun(X51,X50),bool)),pi(X51,X50),X54),X52)),hAPP(fun(X51,fun(X50,bool)),fun(fun(X51,X50),bool),hAPP(fun(X51,bool),fun(fun(X51,fun(X50,bool)),fun(fun(X51,X50),bool)),pi(X51,X50),X54),X53))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_646])])])]) ).

fof(c_0_1255,plain,
    ! [X48,X49,X50,X51,X52,X53] :
      ( ( ~ hBOOL(hAPP(fun(fun(X49,X48),bool),bool,hAPP(fun(X49,X48),fun(fun(fun(X49,X48),bool),bool),member(fun(X49,X48)),X51),hAPP(fun(X49,fun(X48,bool)),fun(fun(X49,X48),bool),hAPP(fun(X49,bool),fun(fun(X49,fun(X48,bool)),fun(fun(X49,X48),bool)),pi(X49,X48),X53),X50)))
        | hBOOL(hAPP(fun(fun(X49,X48),bool),bool,hAPP(fun(X49,X48),fun(fun(fun(X49,X48),bool),bool),member(fun(X49,X48)),X52),hAPP(fun(X49,fun(X48,bool)),fun(fun(X49,X48),bool),hAPP(fun(X49,bool),fun(fun(X49,fun(X48,bool)),fun(fun(X49,X48),bool)),pi(X49,X48),X53),X50)))
        | hBOOL(hAPP(fun(X49,bool),bool,hAPP(X49,fun(fun(X49,bool),bool),member(X49),esk67_6(X48,X49,X50,X51,X52,X53)),X53)) )
      & ( ~ hBOOL(hAPP(fun(fun(X49,X48),bool),bool,hAPP(fun(X49,X48),fun(fun(fun(X49,X48),bool),bool),member(fun(X49,X48)),X52),hAPP(fun(X49,fun(X48,bool)),fun(fun(X49,X48),bool),hAPP(fun(X49,bool),fun(fun(X49,fun(X48,bool)),fun(fun(X49,X48),bool)),pi(X49,X48),X53),X50)))
        | hBOOL(hAPP(fun(fun(X49,X48),bool),bool,hAPP(fun(X49,X48),fun(fun(fun(X49,X48),bool),bool),member(fun(X49,X48)),X51),hAPP(fun(X49,fun(X48,bool)),fun(fun(X49,X48),bool),hAPP(fun(X49,bool),fun(fun(X49,fun(X48,bool)),fun(fun(X49,X48),bool)),pi(X49,X48),X53),X50)))
        | hBOOL(hAPP(fun(X49,bool),bool,hAPP(X49,fun(fun(X49,bool),bool),member(X49),esk67_6(X48,X49,X50,X51,X52,X53)),X53)) )
      & ( ~ hBOOL(hAPP(fun(fun(X49,X48),bool),bool,hAPP(fun(X49,X48),fun(fun(fun(X49,X48),bool),bool),member(fun(X49,X48)),X51),hAPP(fun(X49,fun(X48,bool)),fun(fun(X49,X48),bool),hAPP(fun(X49,bool),fun(fun(X49,fun(X48,bool)),fun(fun(X49,X48),bool)),pi(X49,X48),X53),X50)))
        | hBOOL(hAPP(fun(fun(X49,X48),bool),bool,hAPP(fun(X49,X48),fun(fun(fun(X49,X48),bool),bool),member(fun(X49,X48)),X52),hAPP(fun(X49,fun(X48,bool)),fun(fun(X49,X48),bool),hAPP(fun(X49,bool),fun(fun(X49,fun(X48,bool)),fun(fun(X49,X48),bool)),pi(X49,X48),X53),X50)))
        | hAPP(X49,X48,X51,esk67_6(X48,X49,X50,X51,X52,X53)) != hAPP(X49,X48,X52,esk67_6(X48,X49,X50,X51,X52,X53)) )
      & ( ~ hBOOL(hAPP(fun(fun(X49,X48),bool),bool,hAPP(fun(X49,X48),fun(fun(fun(X49,X48),bool),bool),member(fun(X49,X48)),X52),hAPP(fun(X49,fun(X48,bool)),fun(fun(X49,X48),bool),hAPP(fun(X49,bool),fun(fun(X49,fun(X48,bool)),fun(fun(X49,X48),bool)),pi(X49,X48),X53),X50)))
        | hBOOL(hAPP(fun(fun(X49,X48),bool),bool,hAPP(fun(X49,X48),fun(fun(fun(X49,X48),bool),bool),member(fun(X49,X48)),X51),hAPP(fun(X49,fun(X48,bool)),fun(fun(X49,X48),bool),hAPP(fun(X49,bool),fun(fun(X49,fun(X48,bool)),fun(fun(X49,X48),bool)),pi(X49,X48),X53),X50)))
        | hAPP(X49,X48,X51,esk67_6(X48,X49,X50,X51,X52,X53)) != hAPP(X49,X48,X52,esk67_6(X48,X49,X50,X51,X52,X53)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_647])])])]) ).

fof(c_0_1256,plain,
    ! [X42,X43,X44,X45,X48,X49,X50,X51,X52,X53,X54,X55] :
      ( ( ~ hBOOL(hAPP(fun(product_prod(X42,X43),bool),bool,hAPP(product_prod(X42,X43),fun(fun(product_prod(X42,X43),bool),bool),member(product_prod(X42,X43)),hAPP(X43,product_prod(X42,X43),hAPP(X42,fun(X43,product_prod(X42,X43)),product_Pair(X42,X43),esk21_4(X42,X43,X44,X45)),esk22_4(X42,X43,X44,X45))),X45))
        | ~ hBOOL(hAPP(fun(product_prod(X42,X43),bool),bool,hAPP(product_prod(X42,X43),fun(fun(product_prod(X42,X43),bool),bool),member(product_prod(X42,X43)),hAPP(X43,product_prod(X42,X43),hAPP(X42,fun(X43,product_prod(X42,X43)),product_Pair(X42,X43),esk21_4(X42,X43,X44,X45)),esk22_4(X42,X43,X44,X45))),X44))
        | ti(fun(product_prod(X42,X43),bool),X45) = ti(fun(product_prod(X42,X43),bool),X44) )
      & ( hBOOL(hAPP(fun(product_prod(X42,X43),bool),bool,hAPP(product_prod(X42,X43),fun(fun(product_prod(X42,X43),bool),bool),member(product_prod(X42,X43)),hAPP(X43,product_prod(X42,X43),hAPP(X42,fun(X43,product_prod(X42,X43)),product_Pair(X42,X43),esk21_4(X42,X43,X44,X45)),esk22_4(X42,X43,X44,X45))),X45))
        | hBOOL(hAPP(fun(product_prod(X42,X43),bool),bool,hAPP(product_prod(X42,X43),fun(fun(product_prod(X42,X43),bool),bool),member(product_prod(X42,X43)),hAPP(X43,product_prod(X42,X43),hAPP(X42,fun(X43,product_prod(X42,X43)),product_Pair(X42,X43),esk21_4(X42,X43,X44,X45)),esk22_4(X42,X43,X44,X45))),X44))
        | ti(fun(product_prod(X42,X43),bool),X45) = ti(fun(product_prod(X42,X43),bool),X44) )
      & ( ~ hBOOL(hAPP(fun(product_prod(X48,X49),bool),bool,hAPP(product_prod(X48,X49),fun(fun(product_prod(X48,X49),bool),bool),member(product_prod(X48,X49)),hAPP(X49,product_prod(X48,X49),hAPP(X48,fun(X49,product_prod(X48,X49)),product_Pair(X48,X49),X52),X53)),X51))
        | hBOOL(hAPP(fun(product_prod(X48,X49),bool),bool,hAPP(product_prod(X48,X49),fun(fun(product_prod(X48,X49),bool),bool),member(product_prod(X48,X49)),hAPP(X49,product_prod(X48,X49),hAPP(X48,fun(X49,product_prod(X48,X49)),product_Pair(X48,X49),X52),X53)),X50))
        | ti(fun(product_prod(X48,X49),bool),X51) != ti(fun(product_prod(X48,X49),bool),X50) )
      & ( ~ hBOOL(hAPP(fun(product_prod(X48,X49),bool),bool,hAPP(product_prod(X48,X49),fun(fun(product_prod(X48,X49),bool),bool),member(product_prod(X48,X49)),hAPP(X49,product_prod(X48,X49),hAPP(X48,fun(X49,product_prod(X48,X49)),product_Pair(X48,X49),X54),X55)),X50))
        | hBOOL(hAPP(fun(product_prod(X48,X49),bool),bool,hAPP(product_prod(X48,X49),fun(fun(product_prod(X48,X49),bool),bool),member(product_prod(X48,X49)),hAPP(X49,product_prod(X48,X49),hAPP(X48,fun(X49,product_prod(X48,X49)),product_Pair(X48,X49),X54),X55)),X51))
        | ti(fun(product_prod(X48,X49),bool),X51) != ti(fun(product_prod(X48,X49),bool),X50) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_648])])])])])]) ).

fof(c_0_1257,axiom,
    hBOOL(hAPP(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),f),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1111136790e_Prof),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_2064824852le_Lin)))),
    c_0_649 ).

fof(c_0_1258,plain,
    ! [X51,X52,X53] :
      ( ( ~ hBOOL(hAPP(fun(X51,bool),bool,finite_finite_1(X51),hAPP(fun(X51,bool),fun(X51,bool),collect(X51),X53)))
        | hBOOL(hAPP(fun(X51,bool),bool,finite_finite_1(X51),hAPP(fun(X51,bool),fun(X51,bool),collect(X51),hAPP(fun(X51,bool),fun(X51,bool),hAPP(fun(X51,fun(bool,bool)),fun(fun(X51,bool),fun(X51,bool)),combs(X51,bool,bool),hAPP(fun(X51,bool),fun(X51,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X51,bool),fun(X51,fun(bool,bool))),combb(bool,fun(bool,bool),X51),fconj),X53)),X52)))) )
      & ( ~ hBOOL(hAPP(fun(X51,bool),bool,finite_finite_1(X51),hAPP(fun(X51,bool),fun(X51,bool),collect(X51),X52)))
        | hBOOL(hAPP(fun(X51,bool),bool,finite_finite_1(X51),hAPP(fun(X51,bool),fun(X51,bool),collect(X51),hAPP(fun(X51,bool),fun(X51,bool),hAPP(fun(X51,fun(bool,bool)),fun(fun(X51,bool),fun(X51,bool)),combs(X51,bool,bool),hAPP(fun(X51,bool),fun(X51,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X51,bool),fun(X51,fun(bool,bool))),combb(bool,fun(bool,bool),X51),fconj),X53)),X52)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_650])])]) ).

fof(c_0_1259,plain,
    ! [X67,X68] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),esk77_2(X67,X68)),hAPP(nat,nat,X68,esk77_2(X67,X68))))
      | hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less_eq(nat)),X68)),X67)))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_651])])]) ).

fof(c_0_1260,plain,
    ! [X44,X45,X46,X47,X48] :
      ( ( hBOOL(hAPP(fun(X45,bool),bool,hAPP(X45,fun(fun(X45,bool),bool),member(X45),esk68_5(X44,X45,X46,X47,X48)),X48))
        | hBOOL(hAPP(fun(fun(X45,X44),bool),bool,hAPP(fun(X45,X44),fun(fun(fun(X45,X44),bool),bool),member(fun(X45,X44)),X46),hAPP(fun(X45,fun(X44,bool)),fun(fun(X45,X44),bool),hAPP(fun(X45,bool),fun(fun(X45,fun(X44,bool)),fun(fun(X45,X44),bool)),pi(X45,X44),X48),X47))) )
      & ( ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(X44,fun(fun(X44,bool),bool),member(X44),hAPP(X45,X44,X46,esk68_5(X44,X45,X46,X47,X48))),hAPP(X45,fun(X44,bool),X47,esk68_5(X44,X45,X46,X47,X48))))
        | hBOOL(hAPP(fun(fun(X45,X44),bool),bool,hAPP(fun(X45,X44),fun(fun(fun(X45,X44),bool),bool),member(fun(X45,X44)),X46),hAPP(fun(X45,fun(X44,bool)),fun(fun(X45,X44),bool),hAPP(fun(X45,bool),fun(fun(X45,fun(X44,bool)),fun(fun(X45,X44),bool)),pi(X45,X44),X48),X47))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_652])])])]) ).

fof(c_0_1261,plain,
    ! [X44,X45,X46,X47,X48] :
      ( ( hBOOL(hAPP(fun(X45,bool),bool,hAPP(X45,fun(fun(X45,bool),bool),member(X45),esk33_5(X44,X45,X46,X47,X48)),X48))
        | hBOOL(hAPP(fun(fun(X45,X44),bool),bool,hAPP(fun(X45,X44),fun(fun(fun(X45,X44),bool),bool),member(fun(X45,X44)),X46),hAPP(fun(X45,fun(X44,bool)),fun(fun(X45,X44),bool),hAPP(fun(X45,bool),fun(fun(X45,fun(X44,bool)),fun(fun(X45,X44),bool)),pi(X45,X44),X48),X47))) )
      & ( ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(X44,fun(fun(X44,bool),bool),member(X44),hAPP(X45,X44,X46,esk33_5(X44,X45,X46,X47,X48))),hAPP(X45,fun(X44,bool),X47,esk33_5(X44,X45,X46,X47,X48))))
        | hBOOL(hAPP(fun(fun(X45,X44),bool),bool,hAPP(fun(X45,X44),fun(fun(fun(X45,X44),bool),bool),member(fun(X45,X44)),X46),hAPP(fun(X45,fun(X44,bool)),fun(fun(X45,X44),bool),hAPP(fun(X45,bool),fun(fun(X45,fun(X44,bool)),fun(fun(X45,X44),bool)),pi(X45,X44),X48),X47))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_653])])])]) ).

fof(c_0_1262,plain,
    ! [X15,X16] :
      ( ( ~ hBOOL(hAPP(X15,bool,hAPP(X15,fun(X15,bool),ord_less(X15),hAPP(X15,X15,hAPP(X15,fun(X15,X15),plus_plus(X15),hAPP(X15,X15,hAPP(X15,fun(X15,X15),plus_plus(X15),one_one(X15)),X16)),X16)),zero_zero(X15)))
        | hBOOL(hAPP(X15,bool,hAPP(X15,fun(X15,bool),ord_less(X15),X16),zero_zero(X15)))
        | ~ hBOOL(hAPP(fun(X15,bool),bool,hAPP(X15,fun(fun(X15,bool),bool),member(X15),X16),ring_1_Ints(X15)))
        | ~ linordered_idom(X15) )
      & ( ~ hBOOL(hAPP(X15,bool,hAPP(X15,fun(X15,bool),ord_less(X15),X16),zero_zero(X15)))
        | hBOOL(hAPP(X15,bool,hAPP(X15,fun(X15,bool),ord_less(X15),hAPP(X15,X15,hAPP(X15,fun(X15,X15),plus_plus(X15),hAPP(X15,X15,hAPP(X15,fun(X15,X15),plus_plus(X15),one_one(X15)),X16)),X16)),zero_zero(X15)))
        | ~ hBOOL(hAPP(fun(X15,bool),bool,hAPP(X15,fun(fun(X15,bool),bool),member(X15),X16),ring_1_Ints(X15)))
        | ~ linordered_idom(X15) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_654])])])]) ).

fof(c_0_1263,plain,
    ! [X44,X45,X46,X47,X48,X49,X50,X51] :
      ( ~ hBOOL(hAPP(fun(fun(X44,bool),X45),bool,hAPP(fun(X44,X45),fun(fun(fun(X44,bool),X45),bool),hAPP(X45,fun(fun(X44,X45),fun(fun(fun(X44,bool),X45),bool)),hAPP(fun(X45,fun(X45,X45)),fun(X45,fun(fun(X44,X45),fun(fun(fun(X44,bool),X45),bool))),finite908156982e_idem(X45,X44),X48),X49),X50),X51))
      | ~ hBOOL(hAPP(fun(X44,bool),bool,finite_finite_1(X44),X47))
      | ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(fun(X44,bool),fun(fun(X44,bool),bool),ord_less_eq(fun(X44,bool)),X46),X47))
      | hAPP(X45,X45,hAPP(X45,fun(X45,X45),X48,hAPP(fun(X44,bool),X45,X51,X46)),hAPP(fun(X44,bool),X45,X51,X47)) = hAPP(fun(X44,bool),X45,X51,X47) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_655])]) ).

fof(c_0_1264,plain,
    ! [X44,X45,X46,X47,X48] :
      ( ( hBOOL(hAPP(fun(X45,bool),bool,hAPP(X45,fun(fun(X45,bool),bool),member(X45),esk65_5(X44,X45,X46,X47,X48)),X48))
        | hBOOL(hAPP(fun(fun(X45,X44),bool),bool,hAPP(fun(X45,X44),fun(fun(fun(X45,X44),bool),bool),member(fun(X45,X44)),X46),hAPP(fun(X45,fun(X44,bool)),fun(fun(X45,X44),bool),hAPP(fun(X45,bool),fun(fun(X45,fun(X44,bool)),fun(fun(X45,X44),bool)),pi(X45,X44),X48),hAPP(fun(X44,bool),fun(X45,fun(X44,bool)),combk(fun(X44,bool),X45),X47)))) )
      & ( ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(X44,fun(fun(X44,bool),bool),member(X44),hAPP(X45,X44,X46,esk65_5(X44,X45,X46,X47,X48))),X47))
        | hBOOL(hAPP(fun(fun(X45,X44),bool),bool,hAPP(fun(X45,X44),fun(fun(fun(X45,X44),bool),bool),member(fun(X45,X44)),X46),hAPP(fun(X45,fun(X44,bool)),fun(fun(X45,X44),bool),hAPP(fun(X45,bool),fun(fun(X45,fun(X44,bool)),fun(fun(X45,X44),bool)),pi(X45,X44),X48),hAPP(fun(X44,bool),fun(X45,fun(X44,bool)),combk(fun(X44,bool),X45),X47)))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_656])])])]) ).

fof(c_0_1265,plain,
    ! [X40,X41,X42,X43,X44,X45,X46,X47] :
      ( ~ hBOOL(hAPP(fun(fun(X40,bool),X41),bool,hAPP(fun(X40,X41),fun(fun(fun(X40,bool),X41),bool),hAPP(X41,fun(fun(X40,X41),fun(fun(fun(X40,bool),X41),bool)),hAPP(fun(X41,fun(X41,X41)),fun(X41,fun(fun(X40,X41),fun(fun(fun(X40,bool),X41),bool))),finite908156982e_idem(X41,X40),X44),X45),X46),X47))
      | ~ hBOOL(hAPP(fun(X40,bool),bool,finite_finite_1(X40),X43))
      | ~ hBOOL(hAPP(fun(X40,bool),bool,hAPP(X40,fun(fun(X40,bool),bool),member(X40),X42),X43))
      | hAPP(X41,X41,hAPP(X41,fun(X41,X41),X44,hAPP(X40,X41,X46,X42)),hAPP(fun(X40,bool),X41,X47,X43)) = hAPP(fun(X40,bool),X41,X47,X43) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_657])]) ).

fof(c_0_1266,plain,
    ! [X44,X45,X46,X47,X48,X49] :
      ( ~ hBOOL(hAPP(fun(fun(X44,X45),bool),bool,hAPP(fun(X44,X45),fun(fun(fun(X44,X45),bool),bool),member(fun(X44,X45)),X47),hAPP(fun(X44,fun(X45,bool)),fun(fun(X44,X45),bool),hAPP(fun(X44,bool),fun(fun(X44,fun(X45,bool)),fun(fun(X44,X45),bool)),pi(X44,X45),X48),hAPP(fun(X45,bool),fun(X44,fun(X45,bool)),combk(fun(X45,bool),X44),X49))))
      | ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(fun(X44,X45),fun(fun(X44,bool),bool),inj_on(X44,X45),X47),X48))
      | ~ hBOOL(hAPP(fun(fun(X45,X44),bool),bool,hAPP(fun(X45,X44),fun(fun(fun(X45,X44),bool),bool),member(fun(X45,X44)),X46),hAPP(fun(X45,fun(X44,bool)),fun(fun(X45,X44),bool),hAPP(fun(X45,bool),fun(fun(X45,fun(X44,bool)),fun(fun(X45,X44),bool)),pi(X45,X44),X49),hAPP(fun(X44,bool),fun(X45,fun(X44,bool)),combk(fun(X44,bool),X45),X48))))
      | ~ hBOOL(hAPP(fun(X45,bool),bool,hAPP(fun(X45,X44),fun(fun(X45,bool),bool),inj_on(X45,X44),X46),X49))
      | ~ hBOOL(hAPP(fun(X44,bool),bool,finite_finite_1(X44),X48))
      | ~ hBOOL(hAPP(fun(X45,bool),bool,finite_finite_1(X45),X49))
      | hAPP(fun(X44,bool),nat,finite_card(X44),X48) = hAPP(fun(X45,bool),nat,finite_card(X45),X49) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_658])]) ).

fof(c_0_1267,plain,
    ! [X27,X28,X29,X30,X32,X36] :
      ( ( ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,X27))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X28),arrow_1111136790e_Prof))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X29),X30)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X28,esk14_4(X27,X28,X29,X30))))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X29),X30)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X27,X28))) )
      & ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),esk15_1(X32)),arrow_1111136790e_Prof))
        | hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,X32)) )
      & ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),esk16_1(X32)),esk17_1(X32))),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),esk15_1(X32),X36)))
        | hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,X32)) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),esk16_1(X32)),esk17_1(X32))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X32,esk15_1(X32))))
        | hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,X32)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_659])])])])])]) ).

fof(c_0_1268,plain,
    ! [X39,X40,X41,X42,X43,X44,X45] :
      ( ~ hBOOL(hAPP(fun(fun(X39,bool),X40),bool,hAPP(fun(X39,X40),fun(fun(fun(X39,bool),X40),bool),hAPP(X40,fun(fun(X39,X40),fun(fun(fun(X39,bool),X40),bool)),hAPP(fun(X40,fun(X40,X40)),fun(X40,fun(fun(X39,X40),fun(fun(fun(X39,bool),X40),bool))),finite908156982e_idem(X40,X39),X42),X43),X44),X45))
      | hAPP(X40,X40,hAPP(X40,fun(X40,X40),X42,X41),X41) = ti(X40,X41) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_660])])])]) ).

fof(c_0_1269,plain,
    ! [X40,X41,X42,X43] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X40,bool),nat,finite_card(X40),hAPP(fun(X41,bool),fun(X40,bool),hAPP(fun(X41,X40),fun(fun(X41,bool),fun(X40,bool)),image(X41,X40),X42),X43))),hAPP(fun(X41,bool),nat,finite_card(X41),X43)))
      | ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(fun(X41,X40),fun(fun(X41,bool),bool),inj_on(X41,X40),X42),X43)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_661])]) ).

fof(c_0_1270,plain,
    ! [X9,X10,X11] :
      ( ti(arrow_490897120le_alt,X10) = ti(arrow_490897120le_alt,X11)
      | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X9),arrow_2064824852le_Lin))
      | hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X9),X10),X11)),arrow_2064824852le_Lin)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_662])]) ).

fof(c_0_1271,plain,
    ! [X9,X10,X11] :
      ( ti(arrow_490897120le_alt,X10) = ti(arrow_490897120le_alt,X11)
      | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X9),arrow_2064824852le_Lin))
      | hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X9),X10),X11)),arrow_2064824852le_Lin)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_663])]) ).

fof(c_0_1272,plain,
    ! [X9,X10,X11] :
      ( ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X9),X10)),X11))
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X10),X9)),X11))
        | ti(arrow_490897120le_alt,X9) = ti(arrow_490897120le_alt,X10)
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X11),arrow_2064824852le_Lin)) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X10),X9)),X11))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X9),X10)),X11))
        | ti(arrow_490897120le_alt,X9) = ti(arrow_490897120le_alt,X10)
        | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X11),arrow_2064824852le_Lin)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_664])])]) ).

fof(c_0_1273,plain,
    ! [X16,X17,X18] :
      ( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X18),arrow_2064824852le_Lin))
      | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X16),X17)),X18))
      | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X17),X16)),X18)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_665])]) ).

fof(c_0_1274,plain,
    ! [X42,X43,X44,X45,X46,X47] :
      ( ( ~ hBOOL(hAPP(fun(X42,bool),bool,hAPP(fun(X42,bool),fun(fun(X42,bool),bool),ord_less_eq(fun(X42,bool)),hAPP(fun(X42,bool),fun(X42,bool),hAPP(fun(X42,fun(fun(X42,bool),bool)),fun(fun(X42,bool),fun(X42,bool)),combc(X42,fun(X42,bool),bool),member(X42)),X43)),hAPP(fun(X42,bool),fun(X42,bool),hAPP(fun(X42,fun(fun(X42,bool),bool)),fun(fun(X42,bool),fun(X42,bool)),combc(X42,fun(X42,bool),bool),member(X42)),X44)))
        | hBOOL(hAPP(fun(X42,bool),bool,hAPP(fun(X42,bool),fun(fun(X42,bool),bool),ord_less_eq(fun(X42,bool)),X43),X44)) )
      & ( ~ hBOOL(hAPP(fun(X45,bool),bool,hAPP(fun(X45,bool),fun(fun(X45,bool),bool),ord_less_eq(fun(X45,bool)),X46),X47))
        | hBOOL(hAPP(fun(X45,bool),bool,hAPP(fun(X45,bool),fun(fun(X45,bool),bool),ord_less_eq(fun(X45,bool)),hAPP(fun(X45,bool),fun(X45,bool),hAPP(fun(X45,fun(fun(X45,bool),bool)),fun(fun(X45,bool),fun(X45,bool)),combc(X45,fun(X45,bool),bool),member(X45)),X46)),hAPP(fun(X45,bool),fun(X45,bool),hAPP(fun(X45,fun(fun(X45,bool),bool)),fun(fun(X45,bool),fun(X45,bool)),combc(X45,fun(X45,bool),bool),member(X45)),X47))) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_666])])])]) ).

fof(c_0_1275,plain,
    ! [X39,X40,X41,X42,X43] :
      ( ~ hBOOL(hAPP(fun(X40,bool),bool,finite_finite_1(X40),hAPP(fun(X41,bool),fun(X40,bool),hAPP(fun(X41,X40),fun(fun(X41,bool),fun(X40,bool)),image(X41,X40),X43),top_top(fun(X41,bool)))))
      | hBOOL(hAPP(fun(X39,bool),bool,finite_finite_1(X39),hAPP(fun(X41,bool),fun(X39,bool),hAPP(fun(X41,X39),fun(fun(X41,bool),fun(X39,bool)),image(X41,X39),hAPP(fun(X41,X40),fun(X41,X39),hAPP(fun(X40,X39),fun(fun(X41,X40),fun(X41,X39)),combb(X40,X39,X41),X42),X43)),top_top(fun(X41,bool))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_667])]) ).

fof(c_0_1276,plain,
    ! [X10,X11,X12,X13,X14,X15,X16,X17] :
      ( ( ti(arrow_490897120le_alt,X10) != ti(arrow_490897120le_alt,X13)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X10),X11)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X12),X13))) )
      & ( ti(arrow_490897120le_alt,X11) != ti(arrow_490897120le_alt,X13)
        | ti(arrow_490897120le_alt,X10) != ti(arrow_490897120le_alt,X11)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X10),X11)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X12),X13))) )
      & ( ti(arrow_490897120le_alt,X11) = ti(arrow_490897120le_alt,X13)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X10),X11)),X12))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X10),X11)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X12),X13))) )
      & ( ti(arrow_490897120le_alt,X15) != ti(arrow_490897120le_alt,X17)
        | ti(arrow_490897120le_alt,X15) = ti(arrow_490897120le_alt,X17)
        | ti(arrow_490897120le_alt,X14) = ti(arrow_490897120le_alt,X17)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X14),X15)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X16),X17))) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X14),X15)),X16))
        | ti(arrow_490897120le_alt,X15) = ti(arrow_490897120le_alt,X17)
        | ti(arrow_490897120le_alt,X14) = ti(arrow_490897120le_alt,X17)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X14),X15)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X16),X17))) )
      & ( ti(arrow_490897120le_alt,X15) != ti(arrow_490897120le_alt,X17)
        | ti(arrow_490897120le_alt,X14) = ti(arrow_490897120le_alt,X15)
        | ti(arrow_490897120le_alt,X14) = ti(arrow_490897120le_alt,X17)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X14),X15)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X16),X17))) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X14),X15)),X16))
        | ti(arrow_490897120le_alt,X14) = ti(arrow_490897120le_alt,X15)
        | ti(arrow_490897120le_alt,X14) = ti(arrow_490897120le_alt,X17)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X14),X15)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X16),X17))) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_668])])])])]) ).

fof(c_0_1277,plain,
    ! [X10,X11,X12,X13,X14,X15,X16,X17] :
      ( ( ti(arrow_490897120le_alt,X11) != ti(arrow_490897120le_alt,X13)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X10),X11)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X12),X13))) )
      & ( ti(arrow_490897120le_alt,X10) != ti(arrow_490897120le_alt,X13)
        | ti(arrow_490897120le_alt,X10) != ti(arrow_490897120le_alt,X11)
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X10),X11)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X12),X13))) )
      & ( ti(arrow_490897120le_alt,X10) = ti(arrow_490897120le_alt,X13)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X10),X11)),X12))
        | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X10),X11)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X12),X13))) )
      & ( ti(arrow_490897120le_alt,X14) != ti(arrow_490897120le_alt,X17)
        | ti(arrow_490897120le_alt,X14) = ti(arrow_490897120le_alt,X17)
        | ti(arrow_490897120le_alt,X15) = ti(arrow_490897120le_alt,X17)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X14),X15)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X16),X17))) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X14),X15)),X16))
        | ti(arrow_490897120le_alt,X14) = ti(arrow_490897120le_alt,X17)
        | ti(arrow_490897120le_alt,X15) = ti(arrow_490897120le_alt,X17)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X14),X15)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X16),X17))) )
      & ( ti(arrow_490897120le_alt,X14) != ti(arrow_490897120le_alt,X17)
        | ti(arrow_490897120le_alt,X14) = ti(arrow_490897120le_alt,X15)
        | ti(arrow_490897120le_alt,X15) = ti(arrow_490897120le_alt,X17)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X14),X15)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X16),X17))) )
      & ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X14),X15)),X16))
        | ti(arrow_490897120le_alt,X14) = ti(arrow_490897120le_alt,X15)
        | ti(arrow_490897120le_alt,X15) = ti(arrow_490897120le_alt,X17)
        | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X14),X15)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X16),X17))) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_669])])])])]) ).

fof(c_0_1278,plain,
    ! [X40,X41,X42,X43,X44] :
      ( ~ hBOOL(hAPP(fun(X40,bool),bool,hAPP(X40,fun(fun(X40,bool),bool),member(X40),X42),hAPP(fun(X41,bool),fun(X40,bool),hAPP(fun(X41,X40),fun(fun(X41,bool),fun(X40,bool)),image(X41,X40),X43),X44)))
      | hBOOL(hAPP(fun(X41,bool),bool,hAPP(X41,fun(fun(X41,bool),bool),member(X41),hAPP(X40,X41,hAPP(fun(X41,X40),fun(X40,X41),hAPP(fun(X41,bool),fun(fun(X41,X40),fun(X40,X41)),hilbert_inv_into(X41,X40),X44),X43),X42)),X44)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_670])]) ).

fof(c_0_1279,plain,
    ! [X58,X59,X60] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk61_3(X58,X59,X60)),esk62_3(X58,X59,X60)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,X60,X58)),X59)),hAPP(nat,nat,X60,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X58),X59)))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,X60,esk61_3(X58,X59,X60))),hAPP(nat,nat,X60,esk62_3(X58,X59,X60))))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,X60,X58)),X59)),hAPP(nat,nat,X60,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X58),X59)))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_671])])])]) ).

fof(c_0_1280,axiom,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,hAPP(nat,arrow_660593299e_indi,hAPP(fun(arrow_660593299e_indi,nat),fun(nat,arrow_660593299e_indi),hAPP(fun(arrow_660593299e_indi,bool),fun(fun(arrow_660593299e_indi,nat),fun(nat,arrow_660593299e_indi)),hilbert_inv_into(arrow_660593299e_indi,nat),top_top(fun(arrow_660593299e_indi,bool))),h),n)))),
    c_0_672 ).

fof(c_0_1281,plain,
    ! [X55,X56,X57,X58] :
      ( ( ~ hBOOL(hAPP(X55,bool,hAPP(X55,fun(X55,bool),ord_less(X55),hAPP(nat,X55,X58,X56)),hAPP(nat,X55,X58,X57)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X56),X57))
        | ~ hBOOL(hAPP(X55,bool,hAPP(X55,fun(X55,bool),ord_less(X55),hAPP(nat,X55,X58,esk91_4(X55,X56,X57,X58))),hAPP(nat,X55,X58,hAPP(nat,nat,suc,esk91_4(X55,X56,X57,X58)))))
        | ~ order(X55) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X56),X57))
        | hBOOL(hAPP(X55,bool,hAPP(X55,fun(X55,bool),ord_less(X55),hAPP(nat,X55,X58,X56)),hAPP(nat,X55,X58,X57)))
        | ~ hBOOL(hAPP(X55,bool,hAPP(X55,fun(X55,bool),ord_less(X55),hAPP(nat,X55,X58,esk91_4(X55,X56,X57,X58))),hAPP(nat,X55,X58,hAPP(nat,nat,suc,esk91_4(X55,X56,X57,X58)))))
        | ~ order(X55) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_673])])])])]) ).

fof(c_0_1282,plain,
    ! [X44,X45,X46,X47,X48] :
      ( ~ hBOOL(hAPP(fun(fun(X44,X45),bool),bool,hAPP(fun(X44,X45),fun(fun(fun(X44,X45),bool),bool),member(fun(X44,X45)),X46),hAPP(fun(X44,fun(X45,bool)),fun(fun(X44,X45),bool),hAPP(fun(X44,bool),fun(fun(X44,fun(X45,bool)),fun(fun(X44,X45),bool)),pi(X44,X45),X47),hAPP(fun(X45,bool),fun(X44,fun(X45,bool)),combk(fun(X45,bool),X44),X48))))
      | hBOOL(hAPP(fun(X45,bool),bool,hAPP(fun(X45,bool),fun(fun(X45,bool),bool),ord_less_eq(fun(X45,bool)),hAPP(fun(X44,bool),fun(X45,bool),hAPP(fun(X44,X45),fun(fun(X44,bool),fun(X45,bool)),image(X44,X45),X46),X47)),X48)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_674])]) ).

fof(c_0_1283,plain,
    ! [X44,X45,X46,X47,X48] :
      ( ( ~ hBOOL(hAPP(fun(X45,bool),bool,hAPP(fun(X45,bool),fun(fun(X45,bool),bool),ord_less_eq(fun(X45,bool)),hAPP(fun(X44,bool),fun(X45,bool),hAPP(fun(X44,X45),fun(fun(X44,bool),fun(X45,bool)),image(X44,X45),X48),X46)),hAPP(fun(X44,bool),fun(X45,bool),hAPP(fun(X44,X45),fun(fun(X44,bool),fun(X45,bool)),image(X44,X45),X48),X47)))
        | hBOOL(hAPP(fun(X44,bool),bool,hAPP(fun(X44,bool),fun(fun(X44,bool),bool),ord_less_eq(fun(X44,bool)),X46),X47))
        | ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(fun(X44,X45),fun(fun(X44,bool),bool),inj_on(X44,X45),X48),top_top(fun(X44,bool)))) )
      & ( ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(fun(X44,bool),fun(fun(X44,bool),bool),ord_less_eq(fun(X44,bool)),X46),X47))
        | hBOOL(hAPP(fun(X45,bool),bool,hAPP(fun(X45,bool),fun(fun(X45,bool),bool),ord_less_eq(fun(X45,bool)),hAPP(fun(X44,bool),fun(X45,bool),hAPP(fun(X44,X45),fun(fun(X44,bool),fun(X45,bool)),image(X44,X45),X48),X46)),hAPP(fun(X44,bool),fun(X45,bool),hAPP(fun(X44,X45),fun(fun(X44,bool),fun(X45,bool)),image(X44,X45),X48),X47)))
        | ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(fun(X44,X45),fun(fun(X44,bool),bool),inj_on(X44,X45),X48),top_top(fun(X44,bool)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_675])])]) ).

fof(c_0_1284,plain,
    ! [X73,X74,X75,X76] :
      ( ~ order(X73)
      | ~ hBOOL(hAPP(X73,bool,hAPP(X73,fun(X73,bool),ord_less(X73),hAPP(nat,X73,X76,esk90_4(X73,X74,X75,X76))),hAPP(nat,X73,X76,hAPP(nat,nat,suc,esk90_4(X73,X74,X75,X76)))))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X74),X75))
      | hBOOL(hAPP(X73,bool,hAPP(X73,fun(X73,bool),ord_less(X73),hAPP(nat,X73,X76,X74)),hAPP(nat,X73,X76,X75))) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_676])])])]) ).

fof(c_0_1285,plain,
    ! [X73,X74,X75,X76] :
      ( ~ order(X73)
      | ~ hBOOL(hAPP(X73,bool,hAPP(X73,fun(X73,bool),ord_less_eq(X73),hAPP(nat,X73,X76,esk89_4(X73,X74,X75,X76))),hAPP(nat,X73,X76,hAPP(nat,nat,suc,esk89_4(X73,X74,X75,X76)))))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X74),X75))
      | hBOOL(hAPP(X73,bool,hAPP(X73,fun(X73,bool),ord_less_eq(X73),hAPP(nat,X73,X76,X74)),hAPP(nat,X73,X76,X75))) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_677])])])]) ).

fof(c_0_1286,plain,
    ! [X58,X59] :
      ( ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),X58),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X59),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X59),hAPP(fun(nat,bool),nat,finite_card(nat),X58)))))
      | X58 = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X59),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X59),hAPP(fun(nat,bool),nat,finite_card(nat),X58))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_678])]) ).

fof(c_0_1287,plain,
    ! [X44,X45,X46,X47,X48] :
      ( ~ hBOOL(hAPP(fun(fun(X44,X45),bool),bool,hAPP(fun(X44,X45),fun(fun(fun(X44,X45),bool),bool),member(fun(X44,X45)),X46),hAPP(fun(X44,fun(X45,bool)),fun(fun(X44,X45),bool),hAPP(fun(X44,bool),fun(fun(X44,fun(X45,bool)),fun(fun(X44,X45),bool)),pi(X44,X45),X47),hAPP(fun(X45,bool),fun(X44,fun(X45,bool)),combk(fun(X45,bool),X44),X48))))
      | ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(fun(X44,X45),fun(fun(X44,bool),bool),inj_on(X44,X45),X46),X47))
      | ~ hBOOL(hAPP(fun(X45,bool),bool,finite_finite_1(X45),X48))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X44,bool),nat,finite_card(X44),X47)),hAPP(fun(X45,bool),nat,finite_card(X45),X48))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_679])]) ).

fof(c_0_1288,plain,
    ! [X40,X41,X42,X43,X44,X45] :
      ( hAPP(X40,X41,hAPP(fun(X41,X40),fun(X40,X41),hAPP(fun(X41,bool),fun(fun(X41,X40),fun(X40,X41)),hilbert_inv_into(X41,X40),X42),X43),X44) != hAPP(X40,X41,hAPP(fun(X41,X40),fun(X40,X41),hAPP(fun(X41,bool),fun(fun(X41,X40),fun(X40,X41)),hilbert_inv_into(X41,X40),X42),X43),X45)
      | ~ hBOOL(hAPP(fun(X40,bool),bool,hAPP(X40,fun(fun(X40,bool),bool),member(X40),X44),hAPP(fun(X41,bool),fun(X40,bool),hAPP(fun(X41,X40),fun(fun(X41,bool),fun(X40,bool)),image(X41,X40),X43),X42)))
      | ~ hBOOL(hAPP(fun(X40,bool),bool,hAPP(X40,fun(fun(X40,bool),bool),member(X40),X45),hAPP(fun(X41,bool),fun(X40,bool),hAPP(fun(X41,X40),fun(fun(X41,bool),fun(X40,bool)),image(X41,X40),X43),X42)))
      | ti(X40,X44) = ti(X40,X45) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_680])]) ).

fof(c_0_1289,plain,
    ! [X44,X45,X46,X47,X48,X49] :
      ( ~ hBOOL(hAPP(fun(fun(X44,X45),bool),bool,hAPP(fun(X44,X45),fun(fun(fun(X44,X45),bool),bool),member(fun(X44,X45)),X47),hAPP(fun(X44,fun(X45,bool)),fun(fun(X44,X45),bool),hAPP(fun(X44,bool),fun(fun(X44,fun(X45,bool)),fun(fun(X44,X45),bool)),pi(X44,X45),X48),hAPP(fun(X45,bool),fun(X44,fun(X45,bool)),combk(fun(X45,bool),X44),X49))))
      | ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(X44,fun(fun(X44,bool),bool),member(X44),X46),X48))
      | hBOOL(hAPP(fun(X45,bool),bool,hAPP(X45,fun(fun(X45,bool),bool),member(X45),hAPP(X44,X45,X47,X46)),X49)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_681])]) ).

fof(c_0_1290,plain,
    ! [X49,X50,X51,X52,X53] :
      ( ~ hBOOL(hAPP(fun(X50,bool),bool,hAPP(fun(X50,bool),fun(fun(X50,bool),bool),ord_less_eq(fun(X50,bool)),X52),X53))
      | hBOOL(hAPP(fun(fun(X50,X49),bool),bool,hAPP(fun(fun(X50,X49),bool),fun(fun(fun(X50,X49),bool),bool),ord_less_eq(fun(fun(X50,X49),bool)),hAPP(fun(X50,fun(X49,bool)),fun(fun(X50,X49),bool),hAPP(fun(X50,bool),fun(fun(X50,fun(X49,bool)),fun(fun(X50,X49),bool)),pi(X50,X49),X53),X51)),hAPP(fun(X50,fun(X49,bool)),fun(fun(X50,X49),bool),hAPP(fun(X50,bool),fun(fun(X50,fun(X49,bool)),fun(fun(X50,X49),bool)),pi(X50,X49),X52),X51))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_682])]) ).

fof(c_0_1291,plain,
    ! [X80,X81,X82,X83,X84] :
      ( ( hBOOL(hAPP(X80,bool,hAPP(X80,fun(X80,bool),ord_less_eq(X80),X83),X81))
        | hBOOL(hAPP(X80,bool,hAPP(X80,fun(X80,bool),ord_less_eq(X80),X82),X81))
        | ~ hBOOL(hAPP(fun(X80,bool),bool,hAPP(fun(X80,bool),fun(fun(X80,bool),bool),ord_less_eq(fun(X80,bool)),hAPP(X80,fun(X80,bool),hAPP(X80,fun(X80,fun(X80,bool)),ord_atLeastLessThan(X80),X81),X82)),hAPP(X80,fun(X80,bool),hAPP(X80,fun(X80,fun(X80,bool)),ord_atLeastLessThan(X80),X83),X84)))
        | ~ linorder(X80) )
      & ( hBOOL(hAPP(X80,bool,hAPP(X80,fun(X80,bool),ord_less_eq(X80),X82),X84))
        | hBOOL(hAPP(X80,bool,hAPP(X80,fun(X80,bool),ord_less_eq(X80),X82),X81))
        | ~ hBOOL(hAPP(fun(X80,bool),bool,hAPP(fun(X80,bool),fun(fun(X80,bool),bool),ord_less_eq(fun(X80,bool)),hAPP(X80,fun(X80,bool),hAPP(X80,fun(X80,fun(X80,bool)),ord_atLeastLessThan(X80),X81),X82)),hAPP(X80,fun(X80,bool),hAPP(X80,fun(X80,fun(X80,bool)),ord_atLeastLessThan(X80),X83),X84)))
        | ~ linorder(X80) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_683])])])]) ).

fof(c_0_1292,plain,
    ! [X40,X41,X42,X43] :
      ( ~ hBOOL(hAPP(fun(X41,bool),bool,finite_finite_1(X41),X43))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X40,bool),nat,finite_card(X40),hAPP(fun(X41,bool),fun(X40,bool),hAPP(fun(X41,X40),fun(fun(X41,bool),fun(X40,bool)),image(X41,X40),X42),X43))),hAPP(fun(X41,bool),nat,finite_card(X41),X43))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_684])]) ).

fof(c_0_1293,plain,
    ! [X40,X41,X42] :
      ( ~ hBOOL(hAPP(fun(X40,bool),bool,finite_finite_1(X40),X42))
      | ~ hBOOL(hAPP(fun(X40,bool),bool,hAPP(fun(X40,bool),fun(fun(X40,bool),bool),ord_less_eq(fun(X40,bool)),hAPP(fun(X40,bool),fun(X40,bool),hAPP(fun(X40,X40),fun(fun(X40,bool),fun(X40,bool)),image(X40,X40),X41),X42)),X42))
      | ~ hBOOL(hAPP(fun(X40,bool),bool,hAPP(fun(X40,X40),fun(fun(X40,bool),bool),inj_on(X40,X40),X41),X42))
      | hAPP(fun(X40,bool),fun(X40,bool),hAPP(fun(X40,X40),fun(fun(X40,bool),fun(X40,bool)),image(X40,X40),X41),X42) = ti(fun(X40,bool),X42) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_685])]) ).

fof(c_0_1294,plain,
    ! [X44,X45,X46,X47,X48,X49] :
      ( ~ hBOOL(hAPP(fun(fun(X44,X45),bool),bool,hAPP(fun(X44,X45),fun(fun(fun(X44,X45),bool),bool),member(fun(X44,X45)),X47),hAPP(fun(X44,fun(X45,bool)),fun(fun(X44,X45),bool),hAPP(fun(X44,bool),fun(fun(X44,fun(X45,bool)),fun(fun(X44,X45),bool)),pi(X44,X45),X48),X49)))
      | ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(X44,fun(fun(X44,bool),bool),member(X44),X46),X48))
      | hBOOL(hAPP(fun(X45,bool),bool,hAPP(X45,fun(fun(X45,bool),bool),member(X45),hAPP(X44,X45,X47,X46)),hAPP(X44,fun(X45,bool),X49,X46))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_686])]) ).

fof(c_0_1295,plain,
    ! [X44,X45,X46,X47,X48,X49] :
      ( ~ hBOOL(hAPP(fun(fun(X44,X45),bool),bool,hAPP(fun(X44,X45),fun(fun(fun(X44,X45),bool),bool),member(fun(X44,X45)),X47),hAPP(fun(X44,fun(X45,bool)),fun(fun(X44,X45),bool),hAPP(fun(X44,bool),fun(fun(X44,fun(X45,bool)),fun(fun(X44,X45),bool)),pi(X44,X45),X48),X49)))
      | hBOOL(hAPP(fun(X45,bool),bool,hAPP(X45,fun(fun(X45,bool),bool),member(X45),hAPP(X44,X45,X47,X46)),hAPP(X44,fun(X45,bool),X49,X46)))
      | ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(X44,fun(fun(X44,bool),bool),member(X44),X46),X48)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_687])]) ).

fof(c_0_1296,plain,
    ! [X82,X83,X84,X85,X86,X88,X89,X90,X91,X92,X93] :
      ( ( hBOOL(hAPP(fun(X83,bool),bool,hAPP(fun(X83,bool),fun(fun(X83,bool),bool),ord_less_eq(fun(X83,bool)),esk102_5(X82,X83,X84,X85,X86)),X86))
        | ~ hBOOL(hAPP(fun(X82,bool),bool,hAPP(fun(X82,bool),fun(fun(X82,bool),bool),ord_less_eq(fun(X82,bool)),X84),hAPP(fun(X83,bool),fun(X82,bool),hAPP(fun(X83,X82),fun(fun(X83,bool),fun(X82,bool)),image(X83,X82),X85),X86))) )
      & ( ti(fun(X82,bool),X84) = hAPP(fun(X83,bool),fun(X82,bool),hAPP(fun(X83,X82),fun(fun(X83,bool),fun(X82,bool)),image(X83,X82),X85),esk102_5(X82,X83,X84,X85,X86))
        | ~ hBOOL(hAPP(fun(X82,bool),bool,hAPP(fun(X82,bool),fun(fun(X82,bool),bool),ord_less_eq(fun(X82,bool)),X84),hAPP(fun(X83,bool),fun(X82,bool),hAPP(fun(X83,X82),fun(fun(X83,bool),fun(X82,bool)),image(X83,X82),X85),X86))) )
      & ( ~ hBOOL(hAPP(fun(X89,bool),bool,hAPP(fun(X89,bool),fun(fun(X89,bool),bool),ord_less_eq(fun(X89,bool)),X93),X92))
        | ti(fun(X88,bool),X90) != hAPP(fun(X89,bool),fun(X88,bool),hAPP(fun(X89,X88),fun(fun(X89,bool),fun(X88,bool)),image(X89,X88),X91),X93)
        | hBOOL(hAPP(fun(X88,bool),bool,hAPP(fun(X88,bool),fun(fun(X88,bool),bool),ord_less_eq(fun(X88,bool)),X90),hAPP(fun(X89,bool),fun(X88,bool),hAPP(fun(X89,X88),fun(fun(X89,bool),fun(X88,bool)),image(X89,X88),X91),X92))) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_688])])])])])]) ).

fof(c_0_1297,plain,
    ! [X44,X45,X46,X47,X48] :
      ( ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(fun(X44,X45),fun(fun(X44,bool),bool),inj_on(X44,X45),X47),X48))
      | ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(fun(X44,bool),fun(fun(X44,bool),bool),ord_less(fun(X44,bool)),X46),X48))
      | hBOOL(hAPP(fun(X45,bool),bool,hAPP(fun(X45,bool),fun(fun(X45,bool),bool),ord_less(fun(X45,bool)),hAPP(fun(X44,bool),fun(X45,bool),hAPP(fun(X44,X45),fun(fun(X44,bool),fun(X45,bool)),image(X44,X45),X47),X46)),hAPP(fun(X44,bool),fun(X45,bool),hAPP(fun(X44,X45),fun(fun(X44,bool),fun(X45,bool)),image(X44,X45),X47),X48))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_689])]) ).

fof(c_0_1298,plain,
    ! [X12,X13] :
      ( ( ~ hBOOL(hAPP(fun(X12,bool),bool,finite_finite_1(X12),hAPP(fun(X12,bool),fun(X12,bool),collect(X12),hAPP(fun(X12,bool),fun(X12,bool),hAPP(fun(bool,bool),fun(fun(X12,bool),fun(X12,bool)),combb(bool,bool,X12),fNot),X13))))
        | hBOOL(hAPP(fun(X12,bool),bool,finite_finite_1(X12),top_top(fun(X12,bool))))
        | ~ hBOOL(hAPP(fun(X12,bool),bool,finite_finite_1(X12),hAPP(fun(X12,bool),fun(X12,bool),collect(X12),X13))) )
      & ( ~ hBOOL(hAPP(fun(X12,bool),bool,finite_finite_1(X12),top_top(fun(X12,bool))))
        | hBOOL(hAPP(fun(X12,bool),bool,finite_finite_1(X12),hAPP(fun(X12,bool),fun(X12,bool),collect(X12),hAPP(fun(X12,bool),fun(X12,bool),hAPP(fun(bool,bool),fun(fun(X12,bool),fun(X12,bool)),combb(bool,bool,X12),fNot),X13))))
        | ~ hBOOL(hAPP(fun(X12,bool),bool,finite_finite_1(X12),hAPP(fun(X12,bool),fun(X12,bool),collect(X12),X13))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_690])])]) ).

fof(c_0_1299,plain,
    ! [X40,X41,X42,X43,X44,X46,X47,X48,X49,X50,X51] :
      ( ( hBOOL(hAPP(fun(X41,bool),bool,hAPP(X41,fun(fun(X41,bool),bool),member(X41),esk101_5(X40,X41,X42,X43,X44)),X44))
        | ~ hBOOL(hAPP(fun(X40,bool),bool,hAPP(X40,fun(fun(X40,bool),bool),member(X40),X42),hAPP(fun(X41,bool),fun(X40,bool),hAPP(fun(X41,X40),fun(fun(X41,bool),fun(X40,bool)),image(X41,X40),X43),X44))) )
      & ( ti(X40,X42) = hAPP(X41,X40,X43,esk101_5(X40,X41,X42,X43,X44))
        | ~ hBOOL(hAPP(fun(X40,bool),bool,hAPP(X40,fun(fun(X40,bool),bool),member(X40),X42),hAPP(fun(X41,bool),fun(X40,bool),hAPP(fun(X41,X40),fun(fun(X41,bool),fun(X40,bool)),image(X41,X40),X43),X44))) )
      & ( ~ hBOOL(hAPP(fun(X47,bool),bool,hAPP(X47,fun(fun(X47,bool),bool),member(X47),X51),X50))
        | ti(X46,X48) != hAPP(X47,X46,X49,X51)
        | hBOOL(hAPP(fun(X46,bool),bool,hAPP(X46,fun(fun(X46,bool),bool),member(X46),X48),hAPP(fun(X47,bool),fun(X46,bool),hAPP(fun(X47,X46),fun(fun(X47,bool),fun(X46,bool)),image(X47,X46),X49),X50))) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_691])])])])])]) ).

fof(c_0_1300,plain,
    ! [X42,X43,X44,X45,X46,X47,X48,X49,X50,X51] :
      ( ( ~ hBOOL(hAPP(X42,bool,hAPP(X43,fun(X42,bool),hAPP(fun(product_prod(X43,X42),bool),fun(X43,fun(X42,bool)),in_rel(X43,X42),X44),X45),X46))
        | hBOOL(hAPP(fun(product_prod(X43,X42),bool),bool,hAPP(product_prod(X43,X42),fun(fun(product_prod(X43,X42),bool),bool),member(product_prod(X43,X42)),hAPP(X42,product_prod(X43,X42),hAPP(X43,fun(X42,product_prod(X43,X42)),product_Pair(X43,X42),X45),X46)),X44)) )
      & ( ~ hBOOL(hAPP(fun(product_prod(X48,X47),bool),bool,hAPP(product_prod(X48,X47),fun(fun(product_prod(X48,X47),bool),bool),member(product_prod(X48,X47)),hAPP(X47,product_prod(X48,X47),hAPP(X48,fun(X47,product_prod(X48,X47)),product_Pair(X48,X47),X50),X51)),X49))
        | hBOOL(hAPP(X47,bool,hAPP(X48,fun(X47,bool),hAPP(fun(product_prod(X48,X47),bool),fun(X48,fun(X47,bool)),in_rel(X48,X47),X49),X50),X51)) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_692])])])]) ).

fof(c_0_1301,plain,
    ! [X40,X41] :
      ( ~ hBOOL(hAPP(fun(X40,bool),bool,finite_finite_1(X40),X41))
      | hBOOL(hAPP(fun(fun(X40,bool),bool),bool,finite_finite_1(fun(X40,bool)),hAPP(fun(fun(X40,bool),bool),fun(fun(X40,bool),bool),collect(fun(X40,bool)),hAPP(fun(X40,bool),fun(fun(X40,bool),bool),hAPP(fun(fun(X40,bool),fun(fun(X40,bool),bool)),fun(fun(X40,bool),fun(fun(X40,bool),bool)),combc(fun(X40,bool),fun(X40,bool),bool),ord_less_eq(fun(X40,bool))),X41)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_693])]) ).

fof(c_0_1302,plain,
    ! [X38,X39,X40,X41] :
      ( ~ hBOOL(hAPP(fun(X39,bool),bool,hAPP(fun(X39,X40),fun(fun(X39,bool),bool),inj_on(X39,X40),X41),top_top(fun(X39,bool))))
      | hBOOL(hAPP(fun(X39,bool),bool,hAPP(fun(X39,fun(X38,X40)),fun(fun(X39,bool),bool),inj_on(X39,fun(X38,X40)),hAPP(fun(X39,X40),fun(X39,fun(X38,X40)),hAPP(fun(X40,fun(X38,X40)),fun(fun(X39,X40),fun(X39,fun(X38,X40))),combb(X40,fun(X38,X40),X39),combk(X40,X38)),X41)),top_top(fun(X39,bool)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_694])]) ).

fof(c_0_1303,plain,
    ! [X9,X10] :
      ( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X10),arrow_2064824852le_Lin))
      | hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X10),X9)),arrow_2064824852le_Lin)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_695])]) ).

fof(c_0_1304,plain,
    ! [X9,X10] :
      ( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X10),arrow_2064824852le_Lin))
      | hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X10),X9)),arrow_2064824852le_Lin)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_696])]) ).

fof(c_0_1305,plain,
    ! [X18,X19,X20,X21,X22,X23,X24] :
      ( ( ~ hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less(X18),hAPP(X18,X18,hAPP(X18,fun(X18,X18),plus_plus(X18),X19),X20)),hAPP(X18,X18,hAPP(X18,fun(X18,X18),plus_plus(X18),X21),X20)))
        | hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less(X18),X19),X21))
        | ~ ordere236663937imp_le(X18) )
      & ( ~ hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less(X18),X22),X24))
        | hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less(X18),hAPP(X18,X18,hAPP(X18,fun(X18,X18),plus_plus(X18),X22),X23)),hAPP(X18,X18,hAPP(X18,fun(X18,X18),plus_plus(X18),X24),X23)))
        | ~ ordere236663937imp_le(X18) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_697])])])])]) ).

fof(c_0_1306,plain,
    ! [X18,X19,X20,X21,X22,X23,X24] :
      ( ( ~ hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less(X18),hAPP(X18,X18,hAPP(X18,fun(X18,X18),plus_plus(X18),X19),X20)),hAPP(X18,X18,hAPP(X18,fun(X18,X18),plus_plus(X18),X19),X21)))
        | hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less(X18),X20),X21))
        | ~ ordere236663937imp_le(X18) )
      & ( ~ hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less(X18),X23),X24))
        | hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less(X18),hAPP(X18,X18,hAPP(X18,fun(X18,X18),plus_plus(X18),X22),X23)),hAPP(X18,X18,hAPP(X18,fun(X18,X18),plus_plus(X18),X22),X24)))
        | ~ ordere236663937imp_le(X18) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_698])])])])]) ).

fof(c_0_1307,plain,
    ! [X37,X38,X39,X40] :
      ( ~ ordere236663937imp_le(X37)
      | ~ hBOOL(hAPP(X37,bool,hAPP(X37,fun(X37,bool),ord_less(X37),hAPP(X37,X37,hAPP(X37,fun(X37,X37),plus_plus(X37),X38),X39)),hAPP(X37,X37,hAPP(X37,fun(X37,X37),plus_plus(X37),X40),X39)))
      | hBOOL(hAPP(X37,bool,hAPP(X37,fun(X37,bool),ord_less(X37),X38),X40)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_699])])]) ).

fof(c_0_1308,plain,
    ! [X37,X38,X39,X40] :
      ( ~ ordere236663937imp_le(X37)
      | ~ hBOOL(hAPP(X37,bool,hAPP(X37,fun(X37,bool),ord_less(X37),hAPP(X37,X37,hAPP(X37,fun(X37,X37),plus_plus(X37),X38),X39)),hAPP(X37,X37,hAPP(X37,fun(X37,X37),plus_plus(X37),X38),X40)))
      | hBOOL(hAPP(X37,bool,hAPP(X37,fun(X37,bool),ord_less(X37),X39),X40)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_700])])]) ).

fof(c_0_1309,plain,
    ! [X18,X19,X20,X21,X22,X23,X24] :
      ( ( ~ hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less_eq(X18),hAPP(X18,X18,hAPP(X18,fun(X18,X18),plus_plus(X18),X19),X20)),hAPP(X18,X18,hAPP(X18,fun(X18,X18),plus_plus(X18),X21),X20)))
        | hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less_eq(X18),X19),X21))
        | ~ ordere236663937imp_le(X18) )
      & ( ~ hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less_eq(X18),X22),X24))
        | hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less_eq(X18),hAPP(X18,X18,hAPP(X18,fun(X18,X18),plus_plus(X18),X22),X23)),hAPP(X18,X18,hAPP(X18,fun(X18,X18),plus_plus(X18),X24),X23)))
        | ~ ordere236663937imp_le(X18) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_701])])])])]) ).

fof(c_0_1310,plain,
    ! [X18,X19,X20,X21,X22,X23,X24] :
      ( ( ~ hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less_eq(X18),hAPP(X18,X18,hAPP(X18,fun(X18,X18),plus_plus(X18),X19),X20)),hAPP(X18,X18,hAPP(X18,fun(X18,X18),plus_plus(X18),X19),X21)))
        | hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less_eq(X18),X20),X21))
        | ~ ordere236663937imp_le(X18) )
      & ( ~ hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less_eq(X18),X23),X24))
        | hBOOL(hAPP(X18,bool,hAPP(X18,fun(X18,bool),ord_less_eq(X18),hAPP(X18,X18,hAPP(X18,fun(X18,X18),plus_plus(X18),X22),X23)),hAPP(X18,X18,hAPP(X18,fun(X18,X18),plus_plus(X18),X22),X24)))
        | ~ ordere236663937imp_le(X18) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_702])])])])]) ).

fof(c_0_1311,plain,
    ! [X37,X38,X39,X40] :
      ( ~ ordere236663937imp_le(X37)
      | ~ hBOOL(hAPP(X37,bool,hAPP(X37,fun(X37,bool),ord_less_eq(X37),hAPP(X37,X37,hAPP(X37,fun(X37,X37),plus_plus(X37),X38),X39)),hAPP(X37,X37,hAPP(X37,fun(X37,X37),plus_plus(X37),X40),X39)))
      | hBOOL(hAPP(X37,bool,hAPP(X37,fun(X37,bool),ord_less_eq(X37),X38),X40)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_703])])]) ).

fof(c_0_1312,plain,
    ! [X37,X38,X39,X40] :
      ( ~ ordere236663937imp_le(X37)
      | ~ hBOOL(hAPP(X37,bool,hAPP(X37,fun(X37,bool),ord_less_eq(X37),hAPP(X37,X37,hAPP(X37,fun(X37,X37),plus_plus(X37),X38),X39)),hAPP(X37,X37,hAPP(X37,fun(X37,X37),plus_plus(X37),X38),X40)))
      | hBOOL(hAPP(X37,bool,hAPP(X37,fun(X37,bool),ord_less_eq(X37),X39),X40)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_704])])]) ).

fof(c_0_1313,plain,
    ! [X44,X45,X46,X47,X48] :
      ( ~ hBOOL(hAPP(fun(X45,bool),bool,hAPP(fun(X45,bool),fun(fun(X45,bool),bool),ord_less_eq(fun(X45,bool)),X47),X48))
      | hBOOL(hAPP(fun(X44,bool),bool,hAPP(fun(X44,bool),fun(fun(X44,bool),bool),ord_less_eq(fun(X44,bool)),hAPP(fun(X45,bool),fun(X44,bool),hAPP(fun(X45,X44),fun(fun(X45,bool),fun(X44,bool)),image(X45,X44),X46),X47)),hAPP(fun(X45,bool),fun(X44,bool),hAPP(fun(X45,X44),fun(fun(X45,bool),fun(X44,bool)),image(X45,X44),X46),X48))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_705])]) ).

fof(c_0_1314,plain,
    ! [X58,X59,X60,X61,X62,X63] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X58),X59)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X58),X60)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X59),X60)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X62),X63))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X61),X62)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X61),X63))) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_706])])])]) ).

fof(c_0_1315,plain,
    ! [X58,X59,X60,X61,X62,X63] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X58),X59)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X58),X60)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X59),X60)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X62),X63))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X61),X62)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X61),X63))) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_707])])])]) ).

fof(c_0_1316,plain,
    ! [X39,X40,X41,X42] :
      ( ~ ord(X40)
      | ~ hBOOL(hAPP(X40,bool,hAPP(X40,fun(X40,bool),ord_less_eq(X40),hAPP(X39,X40,X41,esk39_4(X39,X40,X41,X42))),hAPP(X39,X40,X42,esk39_4(X39,X40,X41,X42))))
      | hBOOL(hAPP(fun(X39,X40),bool,hAPP(fun(X39,X40),fun(fun(X39,X40),bool),ord_less_eq(fun(X39,X40)),X41),X42)) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_708])])])]) ).

fof(c_0_1317,plain,
    ! [X39,X40,X41,X42,X43,X44,X45] :
      ( ( ~ hBOOL(hAPP(fun(X39,X40),bool,hAPP(fun(X39,X40),fun(fun(X39,X40),bool),ord_less_eq(fun(X39,X40)),X41),X42))
        | hBOOL(hAPP(X40,bool,hAPP(X40,fun(X40,bool),ord_less_eq(X40),hAPP(X39,X40,X41,X43)),hAPP(X39,X40,X42,X43)))
        | ~ ord(X40) )
      & ( ~ hBOOL(hAPP(X40,bool,hAPP(X40,fun(X40,bool),ord_less_eq(X40),hAPP(X39,X40,X44,esk29_4(X39,X40,X44,X45))),hAPP(X39,X40,X45,esk29_4(X39,X40,X44,X45))))
        | hBOOL(hAPP(fun(X39,X40),bool,hAPP(fun(X39,X40),fun(fun(X39,X40),bool),ord_less_eq(fun(X39,X40)),X44),X45))
        | ~ ord(X40) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_709])])])])])]) ).

fof(c_0_1318,plain,
    ! [X9] :
      ( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X9),arrow_2064824852le_Lin))
      | hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),combk(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),arrow_660593299e_indi),X9)),arrow_1111136790e_Prof)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_710])]) ).

fof(c_0_1319,plain,
    ! [X40,X41,X42,X43,X44] :
      ( ( ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(fun(X41,X40),fun(fun(X41,bool),bool),inj_on(X41,X40),X42),X44))
        | hBOOL(hAPP(fun(X41,bool),bool,hAPP(fun(X41,X40),fun(fun(X41,bool),bool),inj_on(X41,X40),X43),X44))
        | hBOOL(hAPP(fun(X41,bool),bool,hAPP(X41,fun(fun(X41,bool),bool),member(X41),esk71_5(X40,X41,X42,X43,X44)),X44)) )
      & ( ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(fun(X41,X40),fun(fun(X41,bool),bool),inj_on(X41,X40),X43),X44))
        | hBOOL(hAPP(fun(X41,bool),bool,hAPP(fun(X41,X40),fun(fun(X41,bool),bool),inj_on(X41,X40),X42),X44))
        | hBOOL(hAPP(fun(X41,bool),bool,hAPP(X41,fun(fun(X41,bool),bool),member(X41),esk71_5(X40,X41,X42,X43,X44)),X44)) )
      & ( ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(fun(X41,X40),fun(fun(X41,bool),bool),inj_on(X41,X40),X42),X44))
        | hBOOL(hAPP(fun(X41,bool),bool,hAPP(fun(X41,X40),fun(fun(X41,bool),bool),inj_on(X41,X40),X43),X44))
        | hAPP(X41,X40,X42,esk71_5(X40,X41,X42,X43,X44)) != hAPP(X41,X40,X43,esk71_5(X40,X41,X42,X43,X44)) )
      & ( ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(fun(X41,X40),fun(fun(X41,bool),bool),inj_on(X41,X40),X43),X44))
        | hBOOL(hAPP(fun(X41,bool),bool,hAPP(fun(X41,X40),fun(fun(X41,bool),bool),inj_on(X41,X40),X42),X44))
        | hAPP(X41,X40,X42,esk71_5(X40,X41,X42,X43,X44)) != hAPP(X41,X40,X43,esk71_5(X40,X41,X42,X43,X44)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_711])])])]) ).

fof(c_0_1320,plain,
    ! [X43,X44,X45,X46,X47] :
      ( ( ~ hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,X43),X44))
        | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X45),arrow_1111136790e_Prof))
        | hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X43,X45) = hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X45,X44) )
      & ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),esk32_2(X46,X47)),arrow_1111136790e_Prof))
        | hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,X46),X47)) )
      & ( hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X46,esk32_2(X46,X47)) != hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),esk32_2(X46,X47),X47)
        | hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,X46),X47)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_712])])])])])]) ).

fof(c_0_1321,plain,
    ! [X46,X47,X48,X49,X50] :
      ( ~ ordere223160158up_add(X46)
      | ~ hBOOL(hAPP(X46,bool,hAPP(X46,fun(X46,bool),ord_less(X46),X49),X50))
      | ~ hBOOL(hAPP(X46,bool,hAPP(X46,fun(X46,bool),ord_less(X46),X47),X48))
      | hBOOL(hAPP(X46,bool,hAPP(X46,fun(X46,bool),ord_less(X46),hAPP(X46,X46,hAPP(X46,fun(X46,X46),plus_plus(X46),X49),X47)),hAPP(X46,X46,hAPP(X46,fun(X46,X46),plus_plus(X46),X50),X48))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_713])])]) ).

fof(c_0_1322,plain,
    ! [X46,X47,X48,X49,X50] :
      ( ~ ordere779506340up_add(X46)
      | ~ hBOOL(hAPP(X46,bool,hAPP(X46,fun(X46,bool),ord_less_eq(X46),X49),X50))
      | ~ hBOOL(hAPP(X46,bool,hAPP(X46,fun(X46,bool),ord_less_eq(X46),X47),X48))
      | hBOOL(hAPP(X46,bool,hAPP(X46,fun(X46,bool),ord_less_eq(X46),hAPP(X46,X46,hAPP(X46,fun(X46,X46),plus_plus(X46),X49),X47)),hAPP(X46,X46,hAPP(X46,fun(X46,X46),plus_plus(X46),X50),X48))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_714])])]) ).

fof(c_0_1323,plain,
    ! [X46,X47,X48,X49,X50] :
      ( ~ ordere223160158up_add(X46)
      | ~ hBOOL(hAPP(X46,bool,hAPP(X46,fun(X46,bool),ord_less_eq(X46),X49),X50))
      | ~ hBOOL(hAPP(X46,bool,hAPP(X46,fun(X46,bool),ord_less(X46),X47),X48))
      | hBOOL(hAPP(X46,bool,hAPP(X46,fun(X46,bool),ord_less(X46),hAPP(X46,X46,hAPP(X46,fun(X46,X46),plus_plus(X46),X49),X47)),hAPP(X46,X46,hAPP(X46,fun(X46,X46),plus_plus(X46),X50),X48))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_715])])]) ).

fof(c_0_1324,plain,
    ! [X46,X47,X48,X49,X50] :
      ( ~ ordere223160158up_add(X46)
      | ~ hBOOL(hAPP(X46,bool,hAPP(X46,fun(X46,bool),ord_less(X46),X49),X50))
      | ~ hBOOL(hAPP(X46,bool,hAPP(X46,fun(X46,bool),ord_less_eq(X46),X47),X48))
      | hBOOL(hAPP(X46,bool,hAPP(X46,fun(X46,bool),ord_less(X46),hAPP(X46,X46,hAPP(X46,fun(X46,X46),plus_plus(X46),X49),X47)),hAPP(X46,X46,hAPP(X46,fun(X46,X46),plus_plus(X46),X50),X48))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_716])])]) ).

fof(c_0_1325,plain,
    ! [X65,X66,X67] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk63_3(X65,X66,X67)),esk64_3(X65,X66,X67)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X65),X66))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X67,X65)),hAPP(nat,nat,X67,X66))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,X67,esk63_3(X65,X66,X67))),hAPP(nat,nat,X67,esk64_3(X65,X66,X67))))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X65),X66))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X67,X65)),hAPP(nat,nat,X67,X66))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_717])])])]) ).

fof(c_0_1326,plain,
    ! [X62,X63,X64,X65] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X64),X65))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X62),X63))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X64),X62)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X65),X63))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_718])]) ).

fof(c_0_1327,plain,
    ! [X62,X63,X64,X65] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X64),X65))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X62),X63))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X64),X62)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X65),X63))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_719])]) ).

fof(c_0_1328,plain,
    ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab)),
    c_0_720 ).

fof(c_0_1329,plain,
    ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba)),
    c_0_721 ).

fof(c_0_1330,plain,
    ! [X40,X41,X42,X43] :
      ( hAPP(fun(X40,bool),fun(X41,bool),hAPP(fun(X40,X41),fun(fun(X40,bool),fun(X41,bool)),image(X40,X41),X43),top_top(fun(X40,bool))) != top_top(fun(X41,bool))
      | hAPP(fun(X40,bool),fun(X41,bool),hAPP(fun(X40,X41),fun(fun(X40,bool),fun(X41,bool)),image(X40,X41),X43),hAPP(fun(X41,bool),fun(X40,bool),hAPP(fun(X41,X40),fun(fun(X41,bool),fun(X40,bool)),image(X41,X40),hAPP(fun(X40,X41),fun(X41,X40),hAPP(fun(X40,bool),fun(fun(X40,X41),fun(X41,X40)),hilbert_inv_into(X40,X41),top_top(fun(X40,bool))),X43)),X42)) = ti(fun(X41,bool),X42) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_722])]) ).

fof(c_0_1331,plain,
    ! [X40,X41,X42,X43,X44] :
      ( ~ hBOOL(hAPP(fun(X40,bool),bool,hAPP(X40,fun(fun(X40,bool),bool),member(X40),X42),hAPP(fun(X41,bool),fun(X40,bool),hAPP(fun(X41,X40),fun(fun(X41,bool),fun(X40,bool)),image(X41,X40),X43),X44)))
      | hAPP(X41,X40,X43,hAPP(X40,X41,hAPP(fun(X41,X40),fun(X40,X41),hAPP(fun(X41,bool),fun(fun(X41,X40),fun(X40,X41)),hilbert_inv_into(X41,X40),X44),X43),X42)) = ti(X40,X42) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_723])]) ).

fof(c_0_1332,plain,
    ! [X15,X16,X17] :
      ( ( ~ hBOOL(hAPP(X15,bool,hAPP(X15,fun(X15,bool),ord_less(X15),hAPP(X15,X15,hAPP(X15,fun(X15,X15),plus_plus(X15),X16),X16)),zero_zero(X15)))
        | hBOOL(hAPP(X15,bool,hAPP(X15,fun(X15,bool),ord_less(X15),X16),zero_zero(X15)))
        | ~ linordered_idom(X15) )
      & ( ~ hBOOL(hAPP(X15,bool,hAPP(X15,fun(X15,bool),ord_less(X15),X17),zero_zero(X15)))
        | hBOOL(hAPP(X15,bool,hAPP(X15,fun(X15,bool),ord_less(X15),hAPP(X15,X15,hAPP(X15,fun(X15,X15),plus_plus(X15),X17),X17)),zero_zero(X15)))
        | ~ linordered_idom(X15) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_724])])])])]) ).

fof(c_0_1333,plain,
    ! [X15,X16,X17] :
      ( ( ~ hBOOL(hAPP(X15,bool,hAPP(X15,fun(X15,bool),ord_less(X15),hAPP(X15,X15,hAPP(X15,fun(X15,X15),plus_plus(X15),X16),X16)),zero_zero(X15)))
        | hBOOL(hAPP(X15,bool,hAPP(X15,fun(X15,bool),ord_less(X15),X16),zero_zero(X15)))
        | ~ linord219039673up_add(X15) )
      & ( ~ hBOOL(hAPP(X15,bool,hAPP(X15,fun(X15,bool),ord_less(X15),X17),zero_zero(X15)))
        | hBOOL(hAPP(X15,bool,hAPP(X15,fun(X15,bool),ord_less(X15),hAPP(X15,X15,hAPP(X15,fun(X15,X15),plus_plus(X15),X17),X17)),zero_zero(X15)))
        | ~ linord219039673up_add(X15) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_725])])])])]) ).

fof(c_0_1334,plain,
    ! [X15,X16,X17] :
      ( ( ~ hBOOL(hAPP(X15,bool,hAPP(X15,fun(X15,bool),ord_less_eq(X15),hAPP(X15,X15,hAPP(X15,fun(X15,X15),plus_plus(X15),X16),X16)),zero_zero(X15)))
        | hBOOL(hAPP(X15,bool,hAPP(X15,fun(X15,bool),ord_less_eq(X15),X16),zero_zero(X15)))
        | ~ linord219039673up_add(X15) )
      & ( ~ hBOOL(hAPP(X15,bool,hAPP(X15,fun(X15,bool),ord_less_eq(X15),X17),zero_zero(X15)))
        | hBOOL(hAPP(X15,bool,hAPP(X15,fun(X15,bool),ord_less_eq(X15),hAPP(X15,X15,hAPP(X15,fun(X15,X15),plus_plus(X15),X17),X17)),zero_zero(X15)))
        | ~ linord219039673up_add(X15) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_726])])])])]) ).

fof(c_0_1335,plain,
    ! [X16,X17,X18] :
      ( ~ ring_1(X16)
      | ~ hBOOL(hAPP(fun(X16,bool),bool,hAPP(X16,fun(fun(X16,bool),bool),member(X16),X18),ring_1_Ints(X16)))
      | ~ hBOOL(hAPP(fun(X16,bool),bool,hAPP(X16,fun(fun(X16,bool),bool),member(X16),X17),ring_1_Ints(X16)))
      | hBOOL(hAPP(fun(X16,bool),bool,hAPP(X16,fun(fun(X16,bool),bool),member(X16),hAPP(X16,X16,hAPP(X16,fun(X16,X16),plus_plus(X16),X18),X17)),ring_1_Ints(X16))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_727])])]) ).

fof(c_0_1336,plain,
    ! [X44,X45,X46] :
      ( ~ hBOOL(hAPP(fun(X44,bool),bool,finite_finite_1(X44),X46))
      | ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(fun(X44,bool),fun(fun(X44,bool),bool),ord_less_eq(fun(X44,bool)),X45),X46))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X44,bool),nat,finite_card(X44),X45)),hAPP(fun(X44,bool),nat,finite_card(X44),X46)))
      | hBOOL(hAPP(fun(X44,bool),bool,hAPP(fun(X44,bool),fun(fun(X44,bool),bool),ord_less(fun(X44,bool)),X45),X46)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_728])]) ).

fof(c_0_1337,plain,
    ! [X60,X61,X62] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X60),X61)),X62))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X60),X62)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_729])]) ).

fof(c_0_1338,plain,
    ! [X54,X55,X56] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),X55)),X56))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X55),X56)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_730])]) ).

fof(c_0_1339,plain,
    ! [X54,X55,X56] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),X55)),X56))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X56)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_731])]) ).

fof(c_0_1340,plain,
    ! [X54,X55,X56] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X56))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),X55)),X56)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X55),X56))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),X55)),X56)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_732])])]) ).

fof(c_0_1341,plain,
    ! [X37,X38,X39,X40] :
      ( ~ ordere223160158up_add(X37)
      | ~ hBOOL(hAPP(X37,bool,hAPP(X37,fun(X37,bool),ord_less(X37),X39),X40))
      | hBOOL(hAPP(X37,bool,hAPP(X37,fun(X37,bool),ord_less(X37),hAPP(X37,X37,hAPP(X37,fun(X37,X37),plus_plus(X37),X39),X38)),hAPP(X37,X37,hAPP(X37,fun(X37,X37),plus_plus(X37),X40),X38))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_733])])]) ).

fof(c_0_1342,plain,
    ! [X37,X38,X39,X40] :
      ( ~ ordere223160158up_add(X37)
      | ~ hBOOL(hAPP(X37,bool,hAPP(X37,fun(X37,bool),ord_less(X37),X39),X40))
      | hBOOL(hAPP(X37,bool,hAPP(X37,fun(X37,bool),ord_less(X37),hAPP(X37,X37,hAPP(X37,fun(X37,X37),plus_plus(X37),X38),X39)),hAPP(X37,X37,hAPP(X37,fun(X37,X37),plus_plus(X37),X38),X40))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_734])])]) ).

fof(c_0_1343,plain,
    ! [X37,X38,X39,X40] :
      ( ~ ordere779506340up_add(X37)
      | ~ hBOOL(hAPP(X37,bool,hAPP(X37,fun(X37,bool),ord_less_eq(X37),X39),X40))
      | hBOOL(hAPP(X37,bool,hAPP(X37,fun(X37,bool),ord_less_eq(X37),hAPP(X37,X37,hAPP(X37,fun(X37,X37),plus_plus(X37),X39),X38)),hAPP(X37,X37,hAPP(X37,fun(X37,X37),plus_plus(X37),X40),X38))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_735])])]) ).

fof(c_0_1344,plain,
    ! [X37,X38,X39,X40] :
      ( ~ ordere779506340up_add(X37)
      | ~ hBOOL(hAPP(X37,bool,hAPP(X37,fun(X37,bool),ord_less_eq(X37),X39),X40))
      | hBOOL(hAPP(X37,bool,hAPP(X37,fun(X37,bool),ord_less_eq(X37),hAPP(X37,X37,hAPP(X37,fun(X37,X37),plus_plus(X37),X38),X39)),hAPP(X37,X37,hAPP(X37,fun(X37,X37),plus_plus(X37),X38),X40))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_736])])]) ).

fof(c_0_1345,plain,
    ! [X60,X61,X62] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X61),X62))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X61),X60)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X62),X60))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_737])]) ).

fof(c_0_1346,plain,
    ! [X60,X61,X62] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X61),X62))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X61),X60)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X62),X60))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_738])]) ).

fof(c_0_1347,plain,
    ! [X40,X41,X42] :
      ( ~ hBOOL(hAPP(fun(X40,bool),bool,finite_finite_1(X40),X42))
      | ~ hBOOL(hAPP(fun(X40,bool),bool,hAPP(fun(X40,bool),fun(fun(X40,bool),bool),ord_less_eq(fun(X40,bool)),X42),hAPP(fun(X40,bool),fun(X40,bool),hAPP(fun(X40,X40),fun(fun(X40,bool),fun(X40,bool)),image(X40,X40),X41),X42)))
      | hBOOL(hAPP(fun(X40,bool),bool,hAPP(fun(X40,X40),fun(fun(X40,bool),bool),inj_on(X40,X40),X41),X42)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_739])]) ).

fof(c_0_1348,plain,
    ! [X23,X24,X25] :
      ( ~ ordere216010020id_add(X23)
      | ~ hBOOL(hAPP(X23,bool,hAPP(X23,fun(X23,bool),ord_less(X23),X25),zero_zero(X23)))
      | ~ hBOOL(hAPP(X23,bool,hAPP(X23,fun(X23,bool),ord_less_eq(X23),X24),zero_zero(X23)))
      | hBOOL(hAPP(X23,bool,hAPP(X23,fun(X23,bool),ord_less(X23),hAPP(X23,X23,hAPP(X23,fun(X23,X23),plus_plus(X23),X25),X24)),zero_zero(X23))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_740])])]) ).

fof(c_0_1349,plain,
    ! [X23,X24,X25] :
      ( ~ ordere216010020id_add(X23)
      | ~ hBOOL(hAPP(X23,bool,hAPP(X23,fun(X23,bool),ord_less_eq(X23),X25),zero_zero(X23)))
      | ~ hBOOL(hAPP(X23,bool,hAPP(X23,fun(X23,bool),ord_less(X23),X24),zero_zero(X23)))
      | hBOOL(hAPP(X23,bool,hAPP(X23,fun(X23,bool),ord_less(X23),hAPP(X23,X23,hAPP(X23,fun(X23,X23),plus_plus(X23),X25),X24)),zero_zero(X23))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_741])])]) ).

fof(c_0_1350,plain,
    ! [X23,X24,X25] :
      ( ~ ordere216010020id_add(X23)
      | ~ hBOOL(hAPP(X23,bool,hAPP(X23,fun(X23,bool),ord_less(X23),X25),zero_zero(X23)))
      | ~ hBOOL(hAPP(X23,bool,hAPP(X23,fun(X23,bool),ord_less(X23),X24),zero_zero(X23)))
      | hBOOL(hAPP(X23,bool,hAPP(X23,fun(X23,bool),ord_less(X23),hAPP(X23,X23,hAPP(X23,fun(X23,X23),plus_plus(X23),X25),X24)),zero_zero(X23))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_742])])]) ).

fof(c_0_1351,plain,
    ! [X23,X24,X25] :
      ( ~ ordere216010020id_add(X23)
      | ~ hBOOL(hAPP(X23,bool,hAPP(X23,fun(X23,bool),ord_less_eq(X23),X25),zero_zero(X23)))
      | ~ hBOOL(hAPP(X23,bool,hAPP(X23,fun(X23,bool),ord_less_eq(X23),X24),zero_zero(X23)))
      | hBOOL(hAPP(X23,bool,hAPP(X23,fun(X23,bool),ord_less_eq(X23),hAPP(X23,X23,hAPP(X23,fun(X23,X23),plus_plus(X23),X25),X24)),zero_zero(X23))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_743])])]) ).

fof(c_0_1352,plain,
    ! [X40,X41] : hBOOL(hAPP(fun(fun(X40,X40),bool),bool,hAPP(fun(X40,X40),fun(fun(fun(X40,X40),bool),bool),member(fun(X40,X40)),combi(X40)),hAPP(fun(X40,fun(X40,bool)),fun(fun(X40,X40),bool),hAPP(fun(X40,bool),fun(fun(X40,fun(X40,bool)),fun(fun(X40,X40),bool)),pi(X40,X40),X41),hAPP(fun(X40,bool),fun(X40,fun(X40,bool)),combk(fun(X40,bool),X40),X41)))),
    inference(variable_rename,[status(thm)],[c_0_744]) ).

fof(c_0_1353,plain,
    ! [X60,X61] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X60),X61)),X61)),
    inference(variable_rename,[status(thm)],[c_0_745]) ).

fof(c_0_1354,plain,
    ! [X60,X61] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X60),X61)),X60)),
    inference(variable_rename,[status(thm)],[c_0_746]) ).

fof(c_0_1355,plain,
    ! [X40,X41,X42,X43] :
      ( ( ~ hBOOL(hAPP(fun(X40,bool),bool,finite_finite_1(X40),X41))
        | hAPP(fun(X40,bool),nat,finite_card(X40),X41) = hAPP(fun(X40,bool),nat,hAPP(nat,fun(fun(X40,bool),nat),hAPP(fun(X40,nat),fun(nat,fun(fun(X40,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(X40,nat),fun(nat,fun(fun(X40,bool),nat))),finite_fold_image(nat,X40),plus_plus(nat)),hAPP(nat,fun(X40,nat),combk(nat,X40),one_one(nat))),zero_zero(nat)),X41) )
      & ( hBOOL(hAPP(fun(X42,bool),bool,finite_finite_1(X42),X43))
        | hAPP(fun(X42,bool),nat,finite_card(X42),X43) = zero_zero(nat) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_747])])])]) ).

fof(c_0_1356,plain,
    ! [X40,X41] :
      ( ~ hBOOL(hAPP(fun(X40,bool),bool,finite_finite_1(X40),X41))
      | hAPP(fun(X40,bool),nat,finite_card(X40),X41) = hAPP(fun(X40,bool),nat,hAPP(nat,fun(fun(X40,bool),nat),hAPP(fun(X40,nat),fun(nat,fun(fun(X40,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(X40,nat),fun(nat,fun(fun(X40,bool),nat))),finite_fold_image(nat,X40),plus_plus(nat)),hAPP(nat,fun(X40,nat),combk(nat,X40),one_one(nat))),zero_zero(nat)),X41) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_748])]) ).

fof(c_0_1357,plain,
    ! [X44,X45,X46] :
      ( ~ hBOOL(hAPP(fun(X44,bool),bool,finite_finite_1(X44),X46))
      | ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(fun(X44,bool),fun(fun(X44,bool),bool),ord_less_eq(fun(X44,bool)),X45),X46))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X44,bool),nat,finite_card(X44),X46)),hAPP(fun(X44,bool),nat,finite_card(X44),X45)))
      | ti(fun(X44,bool),X45) = ti(fun(X44,bool),X46) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_749])]) ).

fof(c_0_1358,plain,
    ! [X61,X62] : hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,nat),fun(fun(nat,bool),bool),inj_on(nat,nat),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),X61)),X62)),
    inference(variable_rename,[status(thm)],[c_0_750]) ).

fof(c_0_1359,plain,
    ! [X58] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),X58)))),
    inference(variable_rename,[status(thm)],[c_0_751]) ).

fof(c_0_1360,plain,
    ! [X58] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X58)))),
    inference(variable_rename,[status(thm)],[c_0_752]) ).

fof(c_0_1361,plain,
    ! [X46,X47,X48,X49,X50] :
      ( ~ comm_semiring_1(X46)
      | hAPP(X46,X46,hAPP(X46,fun(X46,X46),plus_plus(X46),hAPP(X46,X46,hAPP(X46,fun(X46,X46),plus_plus(X46),X47),X48)),hAPP(X46,X46,hAPP(X46,fun(X46,X46),plus_plus(X46),X49),X50)) = hAPP(X46,X46,hAPP(X46,fun(X46,X46),plus_plus(X46),hAPP(X46,X46,hAPP(X46,fun(X46,X46),plus_plus(X46),X47),X49)),hAPP(X46,X46,hAPP(X46,fun(X46,X46),plus_plus(X46),X48),X50)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_753])])]) ).

fof(c_0_1362,plain,
    ! [X40,X41,X42,X43,X44] :
      ( ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(X41,fun(fun(X41,bool),bool),member(X41),X43),X44))
      | hBOOL(hAPP(fun(X40,bool),bool,hAPP(X40,fun(fun(X40,bool),bool),member(X40),hAPP(X41,X40,X42,X43)),hAPP(fun(X41,bool),fun(X40,bool),hAPP(fun(X41,X40),fun(fun(X41,bool),fun(X40,bool)),image(X41,X40),X42),X44))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_754])]) ).

fof(c_0_1363,plain,
    ! [X55,X56,X57,X58] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X55),X56)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X55))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X56)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X57))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X57),X58))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X58))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X57),X58))) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_755])])])])]) ).

fof(c_0_1364,plain,
    ! [X44,X45,X46,X47] :
      ( ~ hBOOL(hAPP(fun(sum_sum(X44,X45),bool),bool,finite_finite_1(sum_sum(X44,X45)),hAPP(fun(X45,bool),fun(sum_sum(X44,X45),bool),hAPP(fun(X44,bool),fun(fun(X45,bool),fun(sum_sum(X44,X45),bool)),sum_Plus(X44,X45),X46),X47)))
      | hBOOL(hAPP(fun(X45,bool),bool,finite_finite_1(X45),X47)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_756])]) ).

fof(c_0_1365,plain,
    ! [X44,X45,X46,X47] :
      ( ~ hBOOL(hAPP(fun(sum_sum(X44,X45),bool),bool,finite_finite_1(sum_sum(X44,X45)),hAPP(fun(X45,bool),fun(sum_sum(X44,X45),bool),hAPP(fun(X44,bool),fun(fun(X45,bool),fun(sum_sum(X44,X45),bool)),sum_Plus(X44,X45),X46),X47)))
      | hBOOL(hAPP(fun(X44,bool),bool,finite_finite_1(X44),X46)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_757])])])]) ).

fof(c_0_1366,plain,
    ! [X44,X45,X46,X47,X48,X49,X50,X51] :
      ( ( hBOOL(hAPP(fun(X44,bool),bool,finite_finite_1(X44),X46))
        | ~ hBOOL(hAPP(fun(sum_sum(X44,X45),bool),bool,finite_finite_1(sum_sum(X44,X45)),hAPP(fun(X45,bool),fun(sum_sum(X44,X45),bool),hAPP(fun(X44,bool),fun(fun(X45,bool),fun(sum_sum(X44,X45),bool)),sum_Plus(X44,X45),X46),X47))) )
      & ( hBOOL(hAPP(fun(X45,bool),bool,finite_finite_1(X45),X47))
        | ~ hBOOL(hAPP(fun(sum_sum(X44,X45),bool),bool,finite_finite_1(sum_sum(X44,X45)),hAPP(fun(X45,bool),fun(sum_sum(X44,X45),bool),hAPP(fun(X44,bool),fun(fun(X45,bool),fun(sum_sum(X44,X45),bool)),sum_Plus(X44,X45),X46),X47))) )
      & ( ~ hBOOL(hAPP(fun(X48,bool),bool,finite_finite_1(X48),X50))
        | ~ hBOOL(hAPP(fun(X49,bool),bool,finite_finite_1(X49),X51))
        | hBOOL(hAPP(fun(sum_sum(X48,X49),bool),bool,finite_finite_1(sum_sum(X48,X49)),hAPP(fun(X49,bool),fun(sum_sum(X48,X49),bool),hAPP(fun(X48,bool),fun(fun(X49,bool),fun(sum_sum(X48,X49),bool)),sum_Plus(X48,X49),X50),X51))) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_758])])])])]) ).

fof(c_0_1367,plain,
    ! [X51,X52,X53,X54] :
      ( ( hBOOL(hAPP(X51,bool,hAPP(X52,fun(X51,bool),X54,esk50_4(X51,X52,X53,X54)),esk51_4(X51,X52,X53,X54)))
        | hBOOL(hAPP(fun(X52,fun(X51,bool)),bool,hAPP(fun(X52,fun(X51,bool)),fun(fun(X52,fun(X51,bool)),bool),ord_less_eq(fun(X52,fun(X51,bool))),X54),X53)) )
      & ( ~ hBOOL(hAPP(X51,bool,hAPP(X52,fun(X51,bool),X53,esk50_4(X51,X52,X53,X54)),esk51_4(X51,X52,X53,X54)))
        | hBOOL(hAPP(fun(X52,fun(X51,bool)),bool,hAPP(fun(X52,fun(X51,bool)),fun(fun(X52,fun(X51,bool)),bool),ord_less_eq(fun(X52,fun(X51,bool))),X54),X53)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_759])])])]) ).

fof(c_0_1368,plain,
    ! [X23,X24,X25] :
      ( ~ ordere216010020id_add(X23)
      | ~ hBOOL(hAPP(X23,bool,hAPP(X23,fun(X23,bool),ord_less(X23),zero_zero(X23)),X25))
      | ~ hBOOL(hAPP(X23,bool,hAPP(X23,fun(X23,bool),ord_less_eq(X23),zero_zero(X23)),X24))
      | hBOOL(hAPP(X23,bool,hAPP(X23,fun(X23,bool),ord_less(X23),zero_zero(X23)),hAPP(X23,X23,hAPP(X23,fun(X23,X23),plus_plus(X23),X25),X24))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_760])])]) ).

fof(c_0_1369,plain,
    ! [X23,X24,X25] :
      ( ~ ordere216010020id_add(X23)
      | ~ hBOOL(hAPP(X23,bool,hAPP(X23,fun(X23,bool),ord_less_eq(X23),zero_zero(X23)),X25))
      | ~ hBOOL(hAPP(X23,bool,hAPP(X23,fun(X23,bool),ord_less(X23),zero_zero(X23)),X24))
      | hBOOL(hAPP(X23,bool,hAPP(X23,fun(X23,bool),ord_less(X23),zero_zero(X23)),hAPP(X23,X23,hAPP(X23,fun(X23,X23),plus_plus(X23),X25),X24))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_761])])]) ).

fof(c_0_1370,plain,
    ! [X23,X24,X25] :
      ( ~ ordere216010020id_add(X23)
      | ~ hBOOL(hAPP(X23,bool,hAPP(X23,fun(X23,bool),ord_less(X23),zero_zero(X23)),X25))
      | ~ hBOOL(hAPP(X23,bool,hAPP(X23,fun(X23,bool),ord_less(X23),zero_zero(X23)),X24))
      | hBOOL(hAPP(X23,bool,hAPP(X23,fun(X23,bool),ord_less(X23),zero_zero(X23)),hAPP(X23,X23,hAPP(X23,fun(X23,X23),plus_plus(X23),X25),X24))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_762])])]) ).

fof(c_0_1371,plain,
    ! [X23,X24,X25] :
      ( ~ ordere216010020id_add(X23)
      | ~ hBOOL(hAPP(X23,bool,hAPP(X23,fun(X23,bool),ord_less_eq(X23),zero_zero(X23)),X25))
      | ~ hBOOL(hAPP(X23,bool,hAPP(X23,fun(X23,bool),ord_less_eq(X23),zero_zero(X23)),X24))
      | hBOOL(hAPP(X23,bool,hAPP(X23,fun(X23,bool),ord_less_eq(X23),zero_zero(X23)),hAPP(X23,X23,hAPP(X23,fun(X23,X23),plus_plus(X23),X25),X24))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_763])])]) ).

fof(c_0_1372,plain,
    ! [X39,X40,X41,X42,X43] : hAPP(fun(X39,bool),fun(X40,bool),hAPP(fun(X39,X40),fun(fun(X39,bool),fun(X40,bool)),image(X39,X40),hAPP(fun(X39,X41),fun(X39,X40),hAPP(fun(X41,X40),fun(fun(X39,X41),fun(X39,X40)),combb(X41,X40,X39),X42),X43)),top_top(fun(X39,bool))) = hAPP(fun(X41,bool),fun(X40,bool),hAPP(fun(X41,X40),fun(fun(X41,bool),fun(X40,bool)),image(X41,X40),X42),hAPP(fun(X39,bool),fun(X41,bool),hAPP(fun(X39,X41),fun(fun(X39,bool),fun(X41,bool)),image(X39,X41),X43),top_top(fun(X39,bool)))),
    inference(variable_rename,[status(thm)],[c_0_764]) ).

fof(c_0_1373,plain,
    ! [X27,X28] :
      ( ( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),esk26_2(X27,X28)),arrow_2064824852le_Lin))
        | ti(arrow_490897120le_alt,X27) = ti(arrow_490897120le_alt,X28) )
      & ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X27),X28)),esk26_2(X27,X28)))
        | ti(arrow_490897120le_alt,X27) = ti(arrow_490897120le_alt,X28) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_765])])])]) ).

fof(c_0_1374,plain,
    ! [X37,X38,X39,X40] :
      ( ~ ordere216010020id_add(X37)
      | ~ hBOOL(hAPP(X37,bool,hAPP(X37,fun(X37,bool),ord_less(X37),zero_zero(X37)),X40))
      | ~ hBOOL(hAPP(X37,bool,hAPP(X37,fun(X37,bool),ord_less_eq(X37),X38),X39))
      | hBOOL(hAPP(X37,bool,hAPP(X37,fun(X37,bool),ord_less(X37),X38),hAPP(X37,X37,hAPP(X37,fun(X37,X37),plus_plus(X37),X40),X39))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_766])])]) ).

fof(c_0_1375,plain,
    ! [X37,X38,X39,X40] :
      ( ~ ordere216010020id_add(X37)
      | ~ hBOOL(hAPP(X37,bool,hAPP(X37,fun(X37,bool),ord_less_eq(X37),zero_zero(X37)),X40))
      | ~ hBOOL(hAPP(X37,bool,hAPP(X37,fun(X37,bool),ord_less(X37),X38),X39))
      | hBOOL(hAPP(X37,bool,hAPP(X37,fun(X37,bool),ord_less(X37),X38),hAPP(X37,X37,hAPP(X37,fun(X37,X37),plus_plus(X37),X40),X39))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_767])])]) ).

fof(c_0_1376,plain,
    ! [X37,X38,X39,X40] :
      ( ~ linordered_semidom(X37)
      | ~ hBOOL(hAPP(X37,bool,hAPP(X37,fun(X37,bool),ord_less(X37),zero_zero(X37)),X40))
      | ~ hBOOL(hAPP(X37,bool,hAPP(X37,fun(X37,bool),ord_less(X37),X38),X39))
      | hBOOL(hAPP(X37,bool,hAPP(X37,fun(X37,bool),ord_less(X37),X38),hAPP(X37,X37,hAPP(X37,fun(X37,X37),plus_plus(X37),X40),X39))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_768])])]) ).

fof(c_0_1377,plain,
    ! [X37,X38,X39,X40] :
      ( ~ ordere216010020id_add(X37)
      | ~ hBOOL(hAPP(X37,bool,hAPP(X37,fun(X37,bool),ord_less_eq(X37),zero_zero(X37)),X40))
      | ~ hBOOL(hAPP(X37,bool,hAPP(X37,fun(X37,bool),ord_less_eq(X37),X38),X39))
      | hBOOL(hAPP(X37,bool,hAPP(X37,fun(X37,bool),ord_less_eq(X37),X38),hAPP(X37,X37,hAPP(X37,fun(X37,X37),plus_plus(X37),X40),X39))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_769])])]) ).

fof(c_0_1378,plain,
    ! [X37,X38,X39,X40] :
      ( ~ ordere216010020id_add(X37)
      | ~ hBOOL(hAPP(X37,bool,hAPP(X37,fun(X37,bool),ord_less_eq(X37),zero_zero(X37)),X40))
      | ~ hBOOL(hAPP(X37,bool,hAPP(X37,fun(X37,bool),ord_less_eq(X37),X38),X39))
      | hBOOL(hAPP(X37,bool,hAPP(X37,fun(X37,bool),ord_less_eq(X37),X38),hAPP(X37,X37,hAPP(X37,fun(X37,X37),plus_plus(X37),X39),X40))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_770])])]) ).

fof(c_0_1379,plain,
    ! [X76,X77,X78] :
      ( ( hBOOL(hAPP(X76,bool,hAPP(X76,fun(X76,bool),ord_less(X76),zero_zero(X76)),esk99_3(X76,X77,X78)))
        | hBOOL(hAPP(X76,bool,hAPP(X76,fun(X76,bool),ord_less_eq(X76),X77),X78))
        | ~ linordered_field(X76) )
      & ( ~ hBOOL(hAPP(X76,bool,hAPP(X76,fun(X76,bool),ord_less_eq(X76),X77),hAPP(X76,X76,hAPP(X76,fun(X76,X76),plus_plus(X76),X78),esk99_3(X76,X77,X78))))
        | hBOOL(hAPP(X76,bool,hAPP(X76,fun(X76,bool),ord_less_eq(X76),X77),X78))
        | ~ linordered_field(X76) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_771])])])])]) ).

fof(c_0_1380,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),esk19_0))
    & hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),esk19_0),arrow_2064824852le_Lin)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_772])])]) ).

fof(c_0_1381,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),esk18_0))
    & hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),esk18_0),arrow_2064824852le_Lin)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_773])])]) ).

fof(c_0_1382,axiom,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba)),
    c_0_774 ).

fof(c_0_1383,axiom,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab)),
    c_0_775 ).

fof(c_0_1384,plain,
    ! [X40,X41,X42,X43,X44,X45] : hAPP(fun(X40,bool),fun(X41,bool),hAPP(fun(X40,X41),fun(fun(X40,bool),fun(X41,bool)),image(X40,X41),X43),hAPP(fun(X42,bool),fun(X40,bool),hAPP(fun(X42,X40),fun(fun(X42,bool),fun(X40,bool)),image(X42,X40),X44),X45)) = hAPP(fun(X42,bool),fun(X41,bool),hAPP(fun(X42,X41),fun(fun(X42,bool),fun(X41,bool)),image(X42,X41),hAPP(fun(X42,X40),fun(X42,X41),hAPP(fun(X40,X41),fun(fun(X42,X40),fun(X42,X41)),combb(X40,X41,X42),X43),X44)),X45),
    inference(variable_rename,[status(thm)],[c_0_776]) ).

fof(c_0_1385,plain,
    ! [X48,X49,X50,X51] :
      ( ( hBOOL(hAPP(X48,bool,hAPP(X48,fun(X48,bool),ord_less(X48),X50),esk38_4(X48,X49,X50,X51)))
        | hBOOL(hAPP(X48,bool,hAPP(X48,fun(X48,bool),ord_less_eq(X48),X51),X49))
        | ~ hBOOL(hAPP(X48,bool,hAPP(X48,fun(X48,bool),ord_less(X48),X50),X51))
        | ~ dense_linorder(X48) )
      & ( hBOOL(hAPP(X48,bool,hAPP(X48,fun(X48,bool),ord_less(X48),esk38_4(X48,X49,X50,X51)),X51))
        | hBOOL(hAPP(X48,bool,hAPP(X48,fun(X48,bool),ord_less_eq(X48),X51),X49))
        | ~ hBOOL(hAPP(X48,bool,hAPP(X48,fun(X48,bool),ord_less(X48),X50),X51))
        | ~ dense_linorder(X48) )
      & ( ~ hBOOL(hAPP(X48,bool,hAPP(X48,fun(X48,bool),ord_less_eq(X48),esk38_4(X48,X49,X50,X51)),X49))
        | hBOOL(hAPP(X48,bool,hAPP(X48,fun(X48,bool),ord_less_eq(X48),X51),X49))
        | ~ hBOOL(hAPP(X48,bool,hAPP(X48,fun(X48,bool),ord_less(X48),X50),X51))
        | ~ dense_linorder(X48) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_777])])])])]) ).

fof(c_0_1386,plain,
    ! [X40,X41,X42,X43,X44,X45] :
      ( ~ hBOOL(hAPP(fun(X40,bool),bool,hAPP(fun(X40,X41),fun(fun(X40,bool),bool),inj_on(X40,X41),X44),X45))
      | hAPP(X40,X41,X44,X42) != hAPP(X40,X41,X44,X43)
      | ~ hBOOL(hAPP(fun(X40,bool),bool,hAPP(X40,fun(fun(X40,bool),bool),member(X40),X42),X45))
      | ~ hBOOL(hAPP(fun(X40,bool),bool,hAPP(X40,fun(fun(X40,bool),bool),member(X40),X43),X45))
      | ti(X40,X42) = ti(X40,X43) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_778])]) ).

fof(c_0_1387,plain,
    ! [X40,X41,X42,X43,X44,X45] :
      ( ( hAPP(X40,X41,X44,X43) != hAPP(X40,X41,X44,X42)
        | ti(X40,X43) = ti(X40,X42)
        | ~ hBOOL(hAPP(fun(X40,bool),bool,hAPP(X40,fun(fun(X40,bool),bool),member(X40),X42),X45))
        | ~ hBOOL(hAPP(fun(X40,bool),bool,hAPP(X40,fun(fun(X40,bool),bool),member(X40),X43),X45))
        | ~ hBOOL(hAPP(fun(X40,bool),bool,hAPP(fun(X40,X41),fun(fun(X40,bool),bool),inj_on(X40,X41),X44),X45)) )
      & ( ti(X40,X43) != ti(X40,X42)
        | hAPP(X40,X41,X44,X43) = hAPP(X40,X41,X44,X42)
        | ~ hBOOL(hAPP(fun(X40,bool),bool,hAPP(X40,fun(fun(X40,bool),bool),member(X40),X42),X45))
        | ~ hBOOL(hAPP(fun(X40,bool),bool,hAPP(X40,fun(fun(X40,bool),bool),member(X40),X43),X45))
        | ~ hBOOL(hAPP(fun(X40,bool),bool,hAPP(fun(X40,X41),fun(fun(X40,bool),bool),inj_on(X40,X41),X44),X45)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_779])])]) ).

fof(c_0_1388,plain,
    ! [X40,X41,X42,X43,X44,X45] :
      ( ~ hBOOL(hAPP(fun(X40,bool),bool,hAPP(fun(X40,X41),fun(fun(X40,bool),bool),inj_on(X40,X41),X44),X45))
      | ti(X40,X42) = ti(X40,X43)
      | ~ hBOOL(hAPP(fun(X40,bool),bool,hAPP(X40,fun(fun(X40,bool),bool),member(X40),X42),X45))
      | ~ hBOOL(hAPP(fun(X40,bool),bool,hAPP(X40,fun(fun(X40,bool),bool),member(X40),X43),X45))
      | hAPP(X40,X41,X44,X42) != hAPP(X40,X41,X44,X43) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_780])]) ).

fof(c_0_1389,plain,
    ! [X40,X41,X42,X43,X44,X45,X46,X47,X48,X49] :
      ( ( ~ hBOOL(hAPP(fun(X40,bool),bool,hAPP(fun(X40,X41),fun(fun(X40,bool),bool),inj_on(X40,X41),X42),X43))
        | ~ hBOOL(hAPP(fun(X40,bool),bool,hAPP(X40,fun(fun(X40,bool),bool),member(X40),X44),X43))
        | ~ hBOOL(hAPP(fun(X40,bool),bool,hAPP(X40,fun(fun(X40,bool),bool),member(X40),X45),X43))
        | hAPP(X40,X41,X42,X44) != hAPP(X40,X41,X42,X45)
        | ti(X40,X44) = ti(X40,X45) )
      & ( hBOOL(hAPP(fun(X46,bool),bool,hAPP(X46,fun(fun(X46,bool),bool),member(X46),esk30_4(X46,X47,X48,X49)),X49))
        | hBOOL(hAPP(fun(X46,bool),bool,hAPP(fun(X46,X47),fun(fun(X46,bool),bool),inj_on(X46,X47),X48),X49)) )
      & ( hBOOL(hAPP(fun(X46,bool),bool,hAPP(X46,fun(fun(X46,bool),bool),member(X46),esk31_4(X46,X47,X48,X49)),X49))
        | hBOOL(hAPP(fun(X46,bool),bool,hAPP(fun(X46,X47),fun(fun(X46,bool),bool),inj_on(X46,X47),X48),X49)) )
      & ( hAPP(X46,X47,X48,esk30_4(X46,X47,X48,X49)) = hAPP(X46,X47,X48,esk31_4(X46,X47,X48,X49))
        | hBOOL(hAPP(fun(X46,bool),bool,hAPP(fun(X46,X47),fun(fun(X46,bool),bool),inj_on(X46,X47),X48),X49)) )
      & ( ti(X46,esk30_4(X46,X47,X48,X49)) != ti(X46,esk31_4(X46,X47,X48,X49))
        | hBOOL(hAPP(fun(X46,bool),bool,hAPP(fun(X46,X47),fun(fun(X46,bool),bool),inj_on(X46,X47),X48),X49)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_781])])])])])]) ).

fof(c_0_1390,plain,
    ! [X40,X41,X42,X43,X44,X45] :
      ( ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(X41,fun(fun(X41,bool),bool),member(X41),X44),X45))
      | ti(X40,X42) != hAPP(X41,X40,X43,X44)
      | hBOOL(hAPP(fun(X40,bool),bool,hAPP(X40,fun(fun(X40,bool),bool),member(X40),X42),hAPP(fun(X41,bool),fun(X40,bool),hAPP(fun(X41,X40),fun(fun(X41,bool),fun(X40,bool)),image(X41,X40),X43),X45))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_782])]) ).

fof(c_0_1391,plain,
    ! [X40,X41,X42,X43,X44,X45] :
      ( ti(X40,X43) != hAPP(X41,X40,X44,X45)
      | ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(X41,fun(fun(X41,bool),bool),member(X41),X45),X42))
      | hBOOL(hAPP(fun(X40,bool),bool,hAPP(X40,fun(fun(X40,bool),bool),member(X40),X43),hAPP(fun(X41,bool),fun(X40,bool),hAPP(fun(X41,X40),fun(fun(X41,bool),fun(X40,bool)),image(X41,X40),X44),X42))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_783])]) ).

fof(c_0_1392,plain,
    ! [X21,X22,X23,X25,X26,X27,X28,X29,X32] :
      ( ( ~ hBOOL(hAPP(product_prod(X21,X22),bool,X23,esk6_3(X21,X22,X23)))
        | hBOOL(hAPP(product_prod(X21,X22),bool,X23,hAPP(X22,product_prod(X21,X22),hAPP(X21,fun(X22,product_prod(X21,X22)),product_Pair(X21,X22),X25),X26))) )
      & ( ~ hBOOL(hAPP(product_prod(X27,X28),bool,X29,hAPP(X28,product_prod(X27,X28),hAPP(X27,fun(X28,product_prod(X27,X28)),product_Pair(X27,X28),esk7_3(X27,X28,X29)),esk8_3(X27,X28,X29))))
        | hBOOL(hAPP(product_prod(X27,X28),bool,X29,X32)) ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_784])])])])]) ).

fof(c_0_1393,plain,
    ! [X15,X16,X17] :
      ( ( ~ hBOOL(hAPP(X15,bool,hAPP(X15,fun(X15,bool),ord_less(X15),zero_zero(X15)),hAPP(X15,X15,hAPP(X15,fun(X15,X15),plus_plus(X15),X16),X16)))
        | hBOOL(hAPP(X15,bool,hAPP(X15,fun(X15,bool),ord_less(X15),zero_zero(X15)),X16))
        | ~ linord219039673up_add(X15) )
      & ( ~ hBOOL(hAPP(X15,bool,hAPP(X15,fun(X15,bool),ord_less(X15),zero_zero(X15)),X17))
        | hBOOL(hAPP(X15,bool,hAPP(X15,fun(X15,bool),ord_less(X15),zero_zero(X15)),hAPP(X15,X15,hAPP(X15,fun(X15,X15),plus_plus(X15),X17),X17)))
        | ~ linord219039673up_add(X15) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_785])])])])]) ).

fof(c_0_1394,plain,
    ! [X15,X16,X17] :
      ( ( ~ hBOOL(hAPP(X15,bool,hAPP(X15,fun(X15,bool),ord_less_eq(X15),zero_zero(X15)),hAPP(X15,X15,hAPP(X15,fun(X15,X15),plus_plus(X15),X16),X16)))
        | hBOOL(hAPP(X15,bool,hAPP(X15,fun(X15,bool),ord_less_eq(X15),zero_zero(X15)),X16))
        | ~ linord219039673up_add(X15) )
      & ( ~ hBOOL(hAPP(X15,bool,hAPP(X15,fun(X15,bool),ord_less_eq(X15),zero_zero(X15)),X17))
        | hBOOL(hAPP(X15,bool,hAPP(X15,fun(X15,bool),ord_less_eq(X15),zero_zero(X15)),hAPP(X15,X15,hAPP(X15,fun(X15,X15),plus_plus(X15),X17),X17)))
        | ~ linord219039673up_add(X15) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_786])])])])]) ).

fof(c_0_1395,plain,
    ! [X40,X41,X42,X43,X44] :
      ( ~ hBOOL(hAPP(fun(X40,bool),bool,hAPP(fun(X40,X41),fun(fun(X40,bool),bool),inj_on(X40,X41),X43),X44))
      | ~ hBOOL(hAPP(fun(X40,bool),bool,hAPP(X40,fun(fun(X40,bool),bool),member(X40),X42),X44))
      | hAPP(X41,X40,hAPP(fun(X40,X41),fun(X41,X40),hAPP(fun(X40,bool),fun(fun(X40,X41),fun(X41,X40)),hilbert_inv_into(X40,X41),X44),X43),hAPP(X40,X41,X43,X42)) = ti(X40,X42) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_787])]) ).

fof(c_0_1396,plain,
    ! [X51,X52,X53,X54,X55,X56] :
      ( ~ hBOOL(hAPP(fun(X51,fun(X52,bool)),bool,hAPP(fun(X51,fun(X52,bool)),fun(fun(X51,fun(X52,bool)),bool),ord_less_eq(fun(X51,fun(X52,bool))),X55),X56))
      | ~ hBOOL(hAPP(X52,bool,hAPP(X51,fun(X52,bool),X55,X53),X54))
      | hBOOL(hAPP(X52,bool,hAPP(X51,fun(X52,bool),X56,X53),X54)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_788])]) ).

fof(c_0_1397,plain,
    ! [X51,X52,X53,X54,X55,X56] :
      ( ~ hBOOL(hAPP(X51,bool,hAPP(X52,fun(X51,bool),X54,X55),X56))
      | ~ hBOOL(hAPP(fun(X52,fun(X51,bool)),bool,hAPP(fun(X52,fun(X51,bool)),fun(fun(X52,fun(X51,bool)),bool),ord_less_eq(fun(X52,fun(X51,bool))),X54),X53))
      | hBOOL(hAPP(X51,bool,hAPP(X52,fun(X51,bool),X53,X55),X56)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_789])]) ).

fof(c_0_1398,plain,
    ! [X44,X45,X46] :
      ( ~ hBOOL(hAPP(fun(X44,bool),bool,finite_finite_1(X44),X46))
      | ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(fun(X44,bool),fun(fun(X44,bool),bool),ord_less_eq(fun(X44,bool)),X45),X46))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X44,bool),nat,finite_card(X44),X45)),hAPP(fun(X44,bool),nat,finite_card(X44),X46))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_790])]) ).

fof(c_0_1399,plain,
    ! [X44,X45,X46] :
      ( ~ hBOOL(hAPP(fun(X44,bool),bool,finite_finite_1(X44),X46))
      | ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(fun(X44,bool),fun(fun(X44,bool),bool),ord_less(fun(X44,bool)),X45),X46))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X44,bool),nat,finite_card(X44),X45)),hAPP(fun(X44,bool),nat,finite_card(X44),X46))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_791])]) ).

fof(c_0_1400,plain,
    ! [X40,X41,X42,X43,X44,X45] :
      ( ~ hBOOL(hAPP(fun(X40,bool),bool,hAPP(fun(X40,X41),fun(fun(X40,bool),bool),inj_on(X40,X41),X44),X45))
      | ~ hBOOL(hAPP(fun(X40,bool),bool,hAPP(X40,fun(fun(X40,bool),bool),member(X40),X43),X45))
      | hAPP(X40,X41,X44,X43) != ti(X41,X42)
      | hAPP(X41,X40,hAPP(fun(X40,X41),fun(X41,X40),hAPP(fun(X40,bool),fun(fun(X40,X41),fun(X41,X40)),hilbert_inv_into(X40,X41),X45),X44),X42) = ti(X40,X43) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_792])]) ).

fof(c_0_1401,plain,
    ! [X55,X56,X57] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X57),X56))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X55,X57),X56))
        | X56 = X57
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X56),X57)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X55,X57),X56))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X55,X57),X56))
        | X56 = X57
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X56),X57)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X57),X56))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X55,X57),X56))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X55,X57),X56))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X56),X57)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X55,X57),X56))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X55,X57),X56))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X55,X57),X56))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X56),X57)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X57),X56))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X55,X57),X56))
        | X56 = X57
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X55,X57),X56)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X55,X57),X56))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X55,X57),X56))
        | X56 = X57
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X55,X57),X56)) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X57),X56))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X55,X57),X56))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X55,X57),X56))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X55,X57),X56)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X55,X57),X56))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X55,X57),X56))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X55,X57),X56))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X55,X57),X56)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_793])])]) ).

fof(c_0_1402,plain,
    ! [X59,X60] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X59),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X59),X60)))),
    inference(variable_rename,[status(thm)],[c_0_794]) ).

fof(c_0_1403,plain,
    ! [X59,X60] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X59),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X60),X59)))),
    inference(variable_rename,[status(thm)],[c_0_795]) ).

fof(c_0_1404,plain,
    ! [X50,X51,X52,X53] :
      ( ~ hBOOL(hAPP(fun(X50,bool),bool,hAPP(fun(X50,bool),fun(fun(X50,bool),bool),ord_less(fun(X50,bool)),X52),X53))
      | ~ hBOOL(hAPP(fun(X50,bool),bool,hAPP(fun(X50,bool),fun(fun(X50,bool),bool),ord_less(fun(X50,bool)),X53),X51))
      | hBOOL(hAPP(fun(X50,bool),bool,hAPP(fun(X50,bool),fun(fun(X50,bool),bool),ord_less(fun(X50,bool)),X52),X51)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_796])]) ).

fof(c_0_1405,plain,
    ! [X50,X51,X52,X53] :
      ( ~ hBOOL(hAPP(fun(X50,bool),bool,hAPP(fun(X50,bool),fun(fun(X50,bool),bool),ord_less_eq(fun(X50,bool)),X52),X53))
      | ~ hBOOL(hAPP(fun(X50,bool),bool,hAPP(fun(X50,bool),fun(fun(X50,bool),bool),ord_less_eq(fun(X50,bool)),X53),X51))
      | hBOOL(hAPP(fun(X50,bool),bool,hAPP(fun(X50,bool),fun(fun(X50,bool),bool),ord_less_eq(fun(X50,bool)),X52),X51)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_797])]) ).

fof(c_0_1406,plain,
    ! [X50,X51,X52,X53] :
      ( ~ hBOOL(hAPP(fun(X50,bool),bool,hAPP(fun(X50,bool),fun(fun(X50,bool),bool),ord_less_eq(fun(X50,bool)),X52),X53))
      | ~ hBOOL(hAPP(fun(X50,bool),bool,hAPP(fun(X50,bool),fun(fun(X50,bool),bool),ord_less(fun(X50,bool)),X53),X51))
      | hBOOL(hAPP(fun(X50,bool),bool,hAPP(fun(X50,bool),fun(fun(X50,bool),bool),ord_less(fun(X50,bool)),X52),X51)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_798])]) ).

fof(c_0_1407,plain,
    ! [X50,X51,X52,X53] :
      ( ~ hBOOL(hAPP(fun(X50,bool),bool,hAPP(fun(X50,bool),fun(fun(X50,bool),bool),ord_less(fun(X50,bool)),X52),X53))
      | ~ hBOOL(hAPP(fun(X50,bool),bool,hAPP(fun(X50,bool),fun(fun(X50,bool),bool),ord_less_eq(fun(X50,bool)),X53),X51))
      | hBOOL(hAPP(fun(X50,bool),bool,hAPP(fun(X50,bool),fun(fun(X50,bool),bool),ord_less(fun(X50,bool)),X52),X51)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_799])]) ).

fof(c_0_1408,plain,
    ! [X54,X55] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X54)),hAPP(nat,nat,suc,X55)))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X55)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_800])]) ).

fof(c_0_1409,plain,
    ! [X55,X56,X57,X58] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X55)),hAPP(nat,nat,suc,X56)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X55),X56)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X57),X58))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X57)),hAPP(nat,nat,suc,X58))) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_801])])])]) ).

fof(c_0_1410,plain,
    ! [X55,X56,X57,X58] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X55)),hAPP(nat,nat,suc,X56)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X55),X56)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X57),X58))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X57)),hAPP(nat,nat,suc,X58))) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_802])])])]) ).

fof(c_0_1411,plain,
    ! [X38,X39,X40,X41] : hBOOL(hAPP(fun(X38,bool),bool,hAPP(X38,fun(fun(X38,bool),bool),member(X38),hAPP(X39,X38,X40,X41)),hAPP(fun(X39,bool),fun(X38,bool),hAPP(fun(X39,X38),fun(fun(X39,bool),fun(X38,bool)),image(X39,X38),X40),top_top(fun(X39,bool))))),
    inference(variable_rename,[status(thm)],[c_0_803]) ).

fof(c_0_1412,plain,
    ! [X44,X45,X46,X47,X48] :
      ( ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(fun(X44,X45),fun(fun(X44,bool),bool),inj_on(X44,X45),X47),X48))
      | ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(fun(X44,bool),fun(fun(X44,bool),bool),ord_less_eq(fun(X44,bool)),X46),X48))
      | hBOOL(hAPP(fun(X44,bool),bool,hAPP(fun(X44,X45),fun(fun(X44,bool),bool),inj_on(X44,X45),X47),X46)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_804])]) ).

fof(c_0_1413,plain,
    ! [X60,X61,X62] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X61),X62))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X62),X60))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X61)),X60)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_805])]) ).

fof(c_0_1414,plain,
    ! [X39,X40,X41,X42] :
      ( ~ hBOOL(hAPP(fun(X39,bool),bool,hAPP(fun(X39,X40),fun(fun(X39,bool),bool),inj_on(X39,X40),X42),top_top(fun(X39,bool))))
      | hAPP(X39,X40,X42,hAPP(X40,X39,X41,esk34_4(X39,X40,X41,X42))) != ti(X40,esk34_4(X39,X40,X41,X42))
      | hAPP(fun(X39,X40),fun(X40,X39),hAPP(fun(X39,bool),fun(fun(X39,X40),fun(X40,X39)),hilbert_inv_into(X39,X40),top_top(fun(X39,bool))),X42) = ti(fun(X40,X39),X41) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_806])])]) ).

fof(c_0_1415,plain,
    ! [X37,X38,X39,X40] :
      ( ~ comm_semiring_1(X37)
      | hAPP(X37,X37,hAPP(X37,fun(X37,X37),plus_plus(X37),hAPP(X37,X37,hAPP(X37,fun(X37,X37),plus_plus(X37),X38),X39)),X40) = hAPP(X37,X37,hAPP(X37,fun(X37,X37),plus_plus(X37),hAPP(X37,X37,hAPP(X37,fun(X37,X37),plus_plus(X37),X38),X40)),X39) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_807])])]) ).

fof(c_0_1416,plain,
    ! [X44,X45,X46,X47] :
      ( ~ hBOOL(hAPP(fun(X45,bool),bool,finite_finite_1(X45),X47))
      | ~ hBOOL(hAPP(fun(X44,bool),bool,finite_finite_1(X44),X46))
      | hBOOL(hAPP(fun(sum_sum(X45,X44),bool),bool,finite_finite_1(sum_sum(X45,X44)),hAPP(fun(X44,bool),fun(sum_sum(X45,X44),bool),hAPP(fun(X45,bool),fun(fun(X44,bool),fun(sum_sum(X45,X44),bool)),sum_Plus(X45,X44),X47),X46))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_808])]) ).

fof(c_0_1417,plain,
    ! [X44,X45,X46,X47] :
      ( ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(fun(X44,bool),fun(fun(X44,bool),bool),ord_less(fun(X44,bool)),X46),X47))
      | ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(X44,fun(fun(X44,bool),bool),member(X44),X45),X46))
      | hBOOL(hAPP(fun(X44,bool),bool,hAPP(X44,fun(fun(X44,bool),bool),member(X44),X45),X47)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_809])]) ).

fof(c_0_1418,plain,
    ! [X44,X45,X46,X47] :
      ( ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(fun(X44,bool),fun(fun(X44,bool),bool),ord_less_eq(fun(X44,bool)),X46),X47))
      | ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(X44,fun(fun(X44,bool),bool),member(X44),X45),X46))
      | hBOOL(hAPP(fun(X44,bool),bool,hAPP(X44,fun(fun(X44,bool),bool),member(X44),X45),X47)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_810])]) ).

fof(c_0_1419,plain,
    ! [X44,X45,X46,X47] :
      ( ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(X44,fun(fun(X44,bool),bool),member(X44),X46),X47))
      | ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(fun(X44,bool),fun(fun(X44,bool),bool),ord_less_eq(fun(X44,bool)),X47),X45))
      | hBOOL(hAPP(fun(X44,bool),bool,hAPP(X44,fun(fun(X44,bool),bool),member(X44),X46),X45)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_811])]) ).

fof(c_0_1420,plain,
    ! [X44,X45,X46,X47] :
      ( ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(fun(X44,bool),fun(fun(X44,bool),bool),ord_less_eq(fun(X44,bool)),X46),X47))
      | ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(X44,fun(fun(X44,bool),bool),member(X44),X45),X46))
      | hBOOL(hAPP(fun(X44,bool),bool,hAPP(X44,fun(fun(X44,bool),bool),member(X44),X45),X47)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_812])]) ).

fof(c_0_1421,plain,
    ! [X44,X45,X46,X47] :
      ( ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(fun(X44,bool),fun(fun(X44,bool),bool),ord_less_eq(fun(X44,bool)),X46),X47))
      | ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(X44,fun(fun(X44,bool),bool),member(X44),X45),X46))
      | hBOOL(hAPP(fun(X44,bool),bool,hAPP(X44,fun(fun(X44,bool),bool),member(X44),X45),X47)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_813])]) ).

fof(c_0_1422,plain,
    ! [X39,X40,X41,X42,X43] :
      ( ~ ord(X40)
      | ~ hBOOL(hAPP(fun(X39,X40),bool,hAPP(fun(X39,X40),fun(fun(X39,X40),bool),ord_less_eq(fun(X39,X40)),X42),X43))
      | hBOOL(hAPP(X40,bool,hAPP(X40,fun(X40,bool),ord_less_eq(X40),hAPP(X39,X40,X42,X41)),hAPP(X39,X40,X43,X41))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_814])])]) ).

fof(c_0_1423,plain,
    ! [X39,X40,X41,X42,X43] :
      ( ~ ord(X40)
      | ~ hBOOL(hAPP(fun(X39,X40),bool,hAPP(fun(X39,X40),fun(fun(X39,X40),bool),ord_less_eq(fun(X39,X40)),X42),X43))
      | hBOOL(hAPP(X40,bool,hAPP(X40,fun(X40,bool),ord_less_eq(X40),hAPP(X39,X40,X42,X41)),hAPP(X39,X40,X43,X41))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_815])])]) ).

fof(c_0_1424,plain,
    ! [X55,X56,X57,X58] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X55),X56))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X56)),X55)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X58)),X57))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X57),X58)) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_816])])])]) ).

fof(c_0_1425,plain,
    ! [X80,X81,X82,X83,X84] :
      ( ~ linorder(X80)
      | hAPP(X80,fun(X80,bool),hAPP(X80,fun(X80,fun(X80,bool)),ord_atLeastLessThan(X80),X81),X82) != hAPP(X80,fun(X80,bool),hAPP(X80,fun(X80,fun(X80,bool)),ord_atLeastLessThan(X80),X83),X84)
      | ~ hBOOL(hAPP(X80,bool,hAPP(X80,fun(X80,bool),ord_less(X80),X81),X82))
      | ~ hBOOL(hAPP(X80,bool,hAPP(X80,fun(X80,bool),ord_less(X80),X83),X84))
      | ti(X80,X82) = ti(X80,X84) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_817])])]) ).

fof(c_0_1426,plain,
    ! [X80,X81,X82,X83,X84] :
      ( ~ linorder(X80)
      | hAPP(X80,fun(X80,bool),hAPP(X80,fun(X80,fun(X80,bool)),ord_atLeastLessThan(X80),X81),X82) != hAPP(X80,fun(X80,bool),hAPP(X80,fun(X80,fun(X80,bool)),ord_atLeastLessThan(X80),X83),X84)
      | ~ hBOOL(hAPP(X80,bool,hAPP(X80,fun(X80,bool),ord_less(X80),X81),X82))
      | ~ hBOOL(hAPP(X80,bool,hAPP(X80,fun(X80,bool),ord_less(X80),X83),X84))
      | ti(X80,X81) = ti(X80,X83) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_818])])]) ).

fof(c_0_1427,plain,
    ! [X80,X81,X82,X83,X84] :
      ( ( ti(X80,X83) = ti(X80,X81)
        | hAPP(X80,fun(X80,bool),hAPP(X80,fun(X80,fun(X80,bool)),ord_atLeastLessThan(X80),X83),X84) != hAPP(X80,fun(X80,bool),hAPP(X80,fun(X80,fun(X80,bool)),ord_atLeastLessThan(X80),X81),X82)
        | ~ hBOOL(hAPP(X80,bool,hAPP(X80,fun(X80,bool),ord_less(X80),X81),X82))
        | ~ hBOOL(hAPP(X80,bool,hAPP(X80,fun(X80,bool),ord_less(X80),X83),X84))
        | ~ linorder(X80) )
      & ( ti(X80,X84) = ti(X80,X82)
        | hAPP(X80,fun(X80,bool),hAPP(X80,fun(X80,fun(X80,bool)),ord_atLeastLessThan(X80),X83),X84) != hAPP(X80,fun(X80,bool),hAPP(X80,fun(X80,fun(X80,bool)),ord_atLeastLessThan(X80),X81),X82)
        | ~ hBOOL(hAPP(X80,bool,hAPP(X80,fun(X80,bool),ord_less(X80),X81),X82))
        | ~ hBOOL(hAPP(X80,bool,hAPP(X80,fun(X80,bool),ord_less(X80),X83),X84))
        | ~ linorder(X80) )
      & ( ti(X80,X83) != ti(X80,X81)
        | ti(X80,X84) != ti(X80,X82)
        | hAPP(X80,fun(X80,bool),hAPP(X80,fun(X80,fun(X80,bool)),ord_atLeastLessThan(X80),X83),X84) = hAPP(X80,fun(X80,bool),hAPP(X80,fun(X80,fun(X80,bool)),ord_atLeastLessThan(X80),X81),X82)
        | ~ hBOOL(hAPP(X80,bool,hAPP(X80,fun(X80,bool),ord_less(X80),X81),X82))
        | ~ hBOOL(hAPP(X80,bool,hAPP(X80,fun(X80,bool),ord_less(X80),X83),X84))
        | ~ linorder(X80) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_819])])])]) ).

fof(c_0_1428,plain,
    ! [X39,X40,X41,X42,X43,X44] :
      ( ( hBOOL(hAPP(fun(X39,X40),bool,hAPP(fun(X39,X40),fun(fun(X39,X40),bool),ord_less_eq(fun(X39,X40)),X41),X42))
        | ~ hBOOL(hAPP(fun(X39,X40),bool,hAPP(fun(X39,X40),fun(fun(X39,X40),bool),ord_less(fun(X39,X40)),X41),X42))
        | ~ ord(X40) )
      & ( ~ hBOOL(hAPP(fun(X39,X40),bool,hAPP(fun(X39,X40),fun(fun(X39,X40),bool),ord_less_eq(fun(X39,X40)),X42),X41))
        | ~ hBOOL(hAPP(fun(X39,X40),bool,hAPP(fun(X39,X40),fun(fun(X39,X40),bool),ord_less(fun(X39,X40)),X41),X42))
        | ~ ord(X40) )
      & ( ~ hBOOL(hAPP(fun(X39,X40),bool,hAPP(fun(X39,X40),fun(fun(X39,X40),bool),ord_less_eq(fun(X39,X40)),X43),X44))
        | hBOOL(hAPP(fun(X39,X40),bool,hAPP(fun(X39,X40),fun(fun(X39,X40),bool),ord_less_eq(fun(X39,X40)),X44),X43))
        | hBOOL(hAPP(fun(X39,X40),bool,hAPP(fun(X39,X40),fun(fun(X39,X40),bool),ord_less(fun(X39,X40)),X43),X44))
        | ~ ord(X40) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_820])])])])]) ).

fof(c_0_1429,plain,
    ! [X44,X45,X46,X47,X48,X49,X50,X51] :
      ( ( ~ hBOOL(hAPP(fun(X45,bool),bool,finite_finite_1(X45),X47))
        | ~ hBOOL(hAPP(fun(X44,bool),bool,finite_finite_1(X44),X46))
        | hAPP(fun(sum_sum(X45,X44),bool),nat,finite_card(sum_sum(X45,X44)),hAPP(fun(X44,bool),fun(sum_sum(X45,X44),bool),hAPP(fun(X45,bool),fun(fun(X44,bool),fun(sum_sum(X45,X44),bool)),sum_Plus(X45,X44),X47),X46)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X45,bool),nat,finite_card(X45),X47)),hAPP(fun(X44,bool),nat,finite_card(X44),X46)) )
      & ( hBOOL(hAPP(fun(X49,bool),bool,finite_finite_1(X49),X51))
        | hAPP(fun(sum_sum(X49,X48),bool),nat,finite_card(sum_sum(X49,X48)),hAPP(fun(X48,bool),fun(sum_sum(X49,X48),bool),hAPP(fun(X49,bool),fun(fun(X48,bool),fun(sum_sum(X49,X48),bool)),sum_Plus(X49,X48),X51),X50)) = zero_zero(nat) )
      & ( hBOOL(hAPP(fun(X48,bool),bool,finite_finite_1(X48),X50))
        | hAPP(fun(sum_sum(X49,X48),bool),nat,finite_card(sum_sum(X49,X48)),hAPP(fun(X48,bool),fun(sum_sum(X49,X48),bool),hAPP(fun(X49,bool),fun(fun(X48,bool),fun(sum_sum(X49,X48),bool)),sum_Plus(X49,X48),X51),X50)) = zero_zero(nat) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_821])])])])]) ).

fof(c_0_1430,plain,
    ! [X44,X45,X46,X47] :
      ( ~ hBOOL(hAPP(fun(X45,bool),bool,finite_finite_1(X45),X47))
      | ~ hBOOL(hAPP(fun(X44,bool),bool,finite_finite_1(X44),X46))
      | hAPP(fun(sum_sum(X45,X44),bool),nat,finite_card(sum_sum(X45,X44)),hAPP(fun(X44,bool),fun(sum_sum(X45,X44),bool),hAPP(fun(X45,bool),fun(fun(X44,bool),fun(sum_sum(X45,X44),bool)),sum_Plus(X45,X44),X47),X46)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X45,bool),nat,finite_card(X45),X47)),hAPP(fun(X44,bool),nat,finite_card(X44),X46)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_822])]) ).

fof(c_0_1431,plain,
    ! [X40,X41,X42,X43] :
      ( ( ~ hBOOL(hAPP(fun(X41,bool),bool,hAPP(fun(X41,X40),fun(fun(X41,bool),bool),inj_on(X41,X40),X42),X43))
        | hAPP(fun(X40,bool),nat,finite_card(X40),hAPP(fun(X41,bool),fun(X40,bool),hAPP(fun(X41,X40),fun(fun(X41,bool),fun(X40,bool)),image(X41,X40),X42),X43)) = hAPP(fun(X41,bool),nat,finite_card(X41),X43)
        | ~ hBOOL(hAPP(fun(X41,bool),bool,finite_finite_1(X41),X43)) )
      & ( hAPP(fun(X40,bool),nat,finite_card(X40),hAPP(fun(X41,bool),fun(X40,bool),hAPP(fun(X41,X40),fun(fun(X41,bool),fun(X40,bool)),image(X41,X40),X42),X43)) != hAPP(fun(X41,bool),nat,finite_card(X41),X43)
        | hBOOL(hAPP(fun(X41,bool),bool,hAPP(fun(X41,X40),fun(fun(X41,bool),bool),inj_on(X41,X40),X42),X43))
        | ~ hBOOL(hAPP(fun(X41,bool),bool,finite_finite_1(X41),X43)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_823])])]) ).

fof(c_0_1432,plain,
    ! [X40,X41,X42,X43] :
      ( ~ hBOOL(hAPP(fun(X41,bool),bool,finite_finite_1(X41),X43))
      | hAPP(fun(X40,bool),nat,finite_card(X40),hAPP(fun(X41,bool),fun(X40,bool),hAPP(fun(X41,X40),fun(fun(X41,bool),fun(X40,bool)),image(X41,X40),X42),X43)) != hAPP(fun(X41,bool),nat,finite_card(X41),X43)
      | hBOOL(hAPP(fun(X41,bool),bool,hAPP(fun(X41,X40),fun(fun(X41,bool),bool),inj_on(X41,X40),X42),X43)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_824])]) ).

fof(c_0_1433,plain,
    ! [X36,X37,X38] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X37),X38))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X37),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X38),X36))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_825])]) ).

fof(c_0_1434,plain,
    ! [X36,X37,X38] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X37),X38))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X37),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X36),X38))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_826])]) ).

fof(c_0_1435,plain,
    ! [X36,X37,X38] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X37),X38))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X37),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X36),X38))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_827])]) ).

fof(c_0_1436,plain,
    ! [X36,X37,X38] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X37),X38))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X37),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X38),X36))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_828])]) ).

fof(c_0_1437,plain,
    ! [X60,X61,X62] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X61),X62))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X61),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X60),X62))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_829])]) ).

fof(c_0_1438,plain,
    ! [X60,X61,X62] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X61),X62))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X61),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X62),X60))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_830])]) ).

fof(c_0_1439,plain,
    ! [X60,X61,X62] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X61),X62))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X61),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X60),X62))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_831])]) ).

fof(c_0_1440,plain,
    ! [X60,X61,X62] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X61),X62))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X61),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X62),X60))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_832])]) ).

fof(c_0_1441,plain,
    ! [X65,X66] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X65),esk94_2(X65,X66)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X65)),X66)) )
      & ( X66 = hAPP(nat,nat,suc,esk94_2(X65,X66))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X65)),X66)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_833])])])]) ).

fof(c_0_1442,plain,
    ! [X55,X56,X57,X58] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X55),X56))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X55)),X56)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X57)),X58))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X57),X58)) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_834])])])]) ).

fof(c_0_1443,plain,
    ! [X55,X56,X57,X58] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X55)),X56))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X55),X56)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X57),X58))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X57)),X58)) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_835])])])]) ).

fof(c_0_1444,plain,
    ! [X54,X55] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X54)),X55))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X55)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_836])]) ).

fof(c_0_1445,plain,
    ! [X54,X55] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X54)),X55))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X55)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_837])]) ).

fof(c_0_1446,plain,
    ! [X54,X55] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X54)),X55))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X55)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_838])]) ).

fof(c_0_1447,plain,
    ! [X38,X39,X40,X41,X42] :
      ( ti(X38,X40) != hAPP(X39,X38,X41,X42)
      | hBOOL(hAPP(fun(X38,bool),bool,hAPP(X38,fun(fun(X38,bool),bool),member(X38),X40),hAPP(fun(X39,bool),fun(X38,bool),hAPP(fun(X39,X38),fun(fun(X39,bool),fun(X38,bool)),image(X39,X38),X41),top_top(fun(X39,bool))))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_839])])])]) ).

fof(c_0_1448,plain,
    ! [X54,X55] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X55))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X54)),hAPP(nat,nat,suc,X55))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_840])]) ).

fof(c_0_1449,plain,
    ! [X44,X45,X46,X47,X48,X49] :
      ( ( hBOOL(hAPP(fun(X44,bool),bool,hAPP(fun(X44,bool),fun(fun(X44,bool),bool),ord_less_eq(fun(X44,bool)),X45),X46))
        | ti(fun(X44,bool),X45) != ti(fun(X44,bool),X46) )
      & ( hBOOL(hAPP(fun(X44,bool),bool,hAPP(fun(X44,bool),fun(fun(X44,bool),bool),ord_less_eq(fun(X44,bool)),X46),X45))
        | ti(fun(X44,bool),X45) != ti(fun(X44,bool),X46) )
      & ( ~ hBOOL(hAPP(fun(X47,bool),bool,hAPP(fun(X47,bool),fun(fun(X47,bool),bool),ord_less_eq(fun(X47,bool)),X48),X49))
        | ~ hBOOL(hAPP(fun(X47,bool),bool,hAPP(fun(X47,bool),fun(fun(X47,bool),bool),ord_less_eq(fun(X47,bool)),X49),X48))
        | ti(fun(X47,bool),X48) = ti(fun(X47,bool),X49) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_841])])])])]) ).

fof(c_0_1450,plain,
    ! [X44,X45,X46] :
      ( ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(fun(X44,bool),fun(fun(X44,bool),bool),ord_less_eq(fun(X44,bool)),X45),X46))
      | ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(fun(X44,bool),fun(fun(X44,bool),bool),ord_less_eq(fun(X44,bool)),X46),X45))
      | ti(fun(X44,bool),X45) = ti(fun(X44,bool),X46) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_842])]) ).

fof(c_0_1451,plain,
    ! [X36,X37,X38,X39] :
      ( ~ order(X36)
      | ~ hBOOL(hAPP(X36,bool,hAPP(X36,fun(X36,bool),ord_less_eq(X36),X38),X39))
      | ~ hBOOL(hAPP(X36,bool,hAPP(X36,fun(X36,bool),ord_less(X36),X37),X38))
      | hBOOL(hAPP(X36,bool,hAPP(X36,fun(X36,bool),ord_less(X36),X37),X39)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_843])])]) ).

fof(c_0_1452,plain,
    ! [X36,X37,X38,X39] :
      ( ~ preorder(X36)
      | ~ hBOOL(hAPP(X36,bool,hAPP(X36,fun(X36,bool),ord_less_eq(X36),X38),X39))
      | ~ hBOOL(hAPP(X36,bool,hAPP(X36,fun(X36,bool),ord_less(X36),X39),X37))
      | hBOOL(hAPP(X36,bool,hAPP(X36,fun(X36,bool),ord_less(X36),X38),X37)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_844])])]) ).

fof(c_0_1453,plain,
    ! [X36,X37,X38,X39] :
      ( ~ order(X36)
      | ~ hBOOL(hAPP(X36,bool,hAPP(X36,fun(X36,bool),ord_less(X36),X38),X39))
      | ~ hBOOL(hAPP(X36,bool,hAPP(X36,fun(X36,bool),ord_less_eq(X36),X37),X38))
      | hBOOL(hAPP(X36,bool,hAPP(X36,fun(X36,bool),ord_less(X36),X37),X39)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_845])])]) ).

fof(c_0_1454,plain,
    ! [X36,X37,X38,X39] :
      ( ~ preorder(X36)
      | ~ hBOOL(hAPP(X36,bool,hAPP(X36,fun(X36,bool),ord_less(X36),X38),X39))
      | ~ hBOOL(hAPP(X36,bool,hAPP(X36,fun(X36,bool),ord_less_eq(X36),X39),X37))
      | hBOOL(hAPP(X36,bool,hAPP(X36,fun(X36,bool),ord_less(X36),X38),X37)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_846])])]) ).

fof(c_0_1455,plain,
    ! [X36,X37,X38,X39] :
      ( ~ preorder(X36)
      | ~ hBOOL(hAPP(X36,bool,hAPP(X36,fun(X36,bool),ord_less_eq(X36),X38),X39))
      | ~ hBOOL(hAPP(X36,bool,hAPP(X36,fun(X36,bool),ord_less_eq(X36),X39),X37))
      | hBOOL(hAPP(X36,bool,hAPP(X36,fun(X36,bool),ord_less_eq(X36),X38),X37)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_847])])]) ).

fof(c_0_1456,plain,
    ! [X36,X37,X38,X39] :
      ( ~ order(X36)
      | ~ hBOOL(hAPP(X36,bool,hAPP(X36,fun(X36,bool),ord_less_eq(X36),X38),X39))
      | ~ hBOOL(hAPP(X36,bool,hAPP(X36,fun(X36,bool),ord_less_eq(X36),X37),X38))
      | hBOOL(hAPP(X36,bool,hAPP(X36,fun(X36,bool),ord_less_eq(X36),X37),X39)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_848])])]) ).

fof(c_0_1457,plain,
    ! [X36,X37,X38,X39] :
      ( ~ preorder(X36)
      | ~ hBOOL(hAPP(X36,bool,hAPP(X36,fun(X36,bool),ord_less(X36),X38),X39))
      | ~ hBOOL(hAPP(X36,bool,hAPP(X36,fun(X36,bool),ord_less(X36),X39),X37))
      | hBOOL(hAPP(X36,bool,hAPP(X36,fun(X36,bool),ord_less(X36),X38),X37)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_849])])]) ).

fof(c_0_1458,plain,
    ! [X36,X37,X38,X39] :
      ( ~ order(X36)
      | ~ hBOOL(hAPP(X36,bool,hAPP(X36,fun(X36,bool),ord_less(X36),X38),X39))
      | ~ hBOOL(hAPP(X36,bool,hAPP(X36,fun(X36,bool),ord_less(X36),X37),X38))
      | hBOOL(hAPP(X36,bool,hAPP(X36,fun(X36,bool),ord_less(X36),X37),X39)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_850])])]) ).

fof(c_0_1459,plain,
    ! [X38,X39,X40,X41] :
      ( ~ hBOOL(hAPP(fun(X38,bool),bool,hAPP(fun(X38,X39),fun(fun(X38,bool),bool),inj_on(X38,X39),X41),top_top(fun(X38,bool))))
      | hAPP(X39,X38,hAPP(fun(X38,X39),fun(X39,X38),hAPP(fun(X38,bool),fun(fun(X38,X39),fun(X39,X38)),hilbert_inv_into(X38,X39),top_top(fun(X38,bool))),X41),hAPP(X38,X39,X41,X40)) = ti(X38,X40) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_851])]) ).

fof(c_0_1460,axiom,
    hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),p),arrow_1111136790e_Prof)),
    c_0_852 ).

fof(c_0_1461,plain,
    ! [X38,X39,X40,X41,X42] :
      ( ~ hBOOL(hAPP(fun(X38,bool),bool,hAPP(fun(X38,X39),fun(fun(X38,bool),bool),inj_on(X38,X39),X42),top_top(fun(X38,bool))))
      | hAPP(X38,X39,X42,X40) != ti(X39,X41)
      | hAPP(X39,X38,hAPP(fun(X38,X39),fun(X39,X38),hAPP(fun(X38,bool),fun(fun(X38,X39),fun(X39,X38)),hilbert_inv_into(X38,X39),top_top(fun(X38,bool))),X42),X41) = ti(X38,X40) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_853])]) ).

fof(c_0_1462,plain,
    ! [X60,X61,X62] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X61),X62))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X62),X60))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X61),X60)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_854])]) ).

fof(c_0_1463,axiom,
    arrow_1111136790e_Prof = hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(arrow_660593299e_indi,bool),fun(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),top_top(fun(arrow_660593299e_indi,bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),arrow_660593299e_indi),arrow_2064824852le_Lin)),
    c_0_855 ).

fof(c_0_1464,plain,
    ! [X62,X63,X64,X65] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X64),X65))
      | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X62),X65) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X64),X63)
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X62),X63)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_856])]) ).

fof(c_0_1465,plain,
    ! [X37,X38,X39,X40] :
      ( ~ comm_semiring_1(X37)
      | hAPP(X37,X37,hAPP(X37,fun(X37,X37),plus_plus(X37),hAPP(X37,X37,hAPP(X37,fun(X37,X37),plus_plus(X37),X38),X39)),X40) = hAPP(X37,X37,hAPP(X37,fun(X37,X37),plus_plus(X37),X38),hAPP(X37,X37,hAPP(X37,fun(X37,X37),plus_plus(X37),X39),X40)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_857])])]) ).

fof(c_0_1466,plain,
    ! [X46,X47,X48,X49] :
      ( ~ comm_semiring_1(X46)
      | hAPP(X46,X46,hAPP(X46,fun(X46,X46),plus_plus(X46),X47),hAPP(X46,X46,hAPP(X46,fun(X46,X46),plus_plus(X46),X48),X49)) = hAPP(X46,X46,hAPP(X46,fun(X46,X46),plus_plus(X46),hAPP(X46,X46,hAPP(X46,fun(X46,X46),plus_plus(X46),X47),X48)),X49) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_858])])]) ).

fof(c_0_1467,plain,
    ! [X37,X38,X39,X40] :
      ( ~ ab_semigroup_add(X37)
      | hAPP(X37,X37,hAPP(X37,fun(X37,X37),plus_plus(X37),hAPP(X37,X37,hAPP(X37,fun(X37,X37),plus_plus(X37),X38),X39)),X40) = hAPP(X37,X37,hAPP(X37,fun(X37,X37),plus_plus(X37),X38),hAPP(X37,X37,hAPP(X37,fun(X37,X37),plus_plus(X37),X39),X40)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_859])])]) ).

fof(c_0_1468,plain,
    ! [X55,X56] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X56),hAPP(nat,nat,suc,X55)))
        | X56 = X55
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X55),X56)) )
      & ( X56 != X55
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X56),hAPP(nat,nat,suc,X55)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X55),X56)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_860])])]) ).

fof(c_0_1469,plain,
    ! [X55,X56,X57,X58] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X55),X56))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X56),hAPP(nat,nat,suc,X55))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X58),hAPP(nat,nat,suc,X57)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X57),X58)) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_861])])])]) ).

fof(c_0_1470,plain,
    ! [X8,X9,X10] :
      ( ( ti(X8,X10) = zero_zero(X8)
        | hAPP(X8,X8,hAPP(X8,fun(X8,X8),plus_plus(X8),X10),X9) != zero_zero(X8)
        | ~ hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less_eq(X8),zero_zero(X8)),X9))
        | ~ hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less_eq(X8),zero_zero(X8)),X10))
        | ~ ordere216010020id_add(X8) )
      & ( ti(X8,X9) = zero_zero(X8)
        | hAPP(X8,X8,hAPP(X8,fun(X8,X8),plus_plus(X8),X10),X9) != zero_zero(X8)
        | ~ hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less_eq(X8),zero_zero(X8)),X9))
        | ~ hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less_eq(X8),zero_zero(X8)),X10))
        | ~ ordere216010020id_add(X8) )
      & ( ti(X8,X10) != zero_zero(X8)
        | ti(X8,X9) != zero_zero(X8)
        | hAPP(X8,X8,hAPP(X8,fun(X8,X8),plus_plus(X8),X10),X9) = zero_zero(X8)
        | ~ hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less_eq(X8),zero_zero(X8)),X9))
        | ~ hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less_eq(X8),zero_zero(X8)),X10))
        | ~ ordere216010020id_add(X8) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_862])])])]) ).

fof(c_0_1471,plain,
    ! [X54,X55,X56] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),X55)),X56) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X55),X56)),
    inference(variable_rename,[status(thm)],[c_0_863]) ).

fof(c_0_1472,plain,
    ! [X54,X55] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X55))
      | hAPP(nat,nat,suc,X54) = X55
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X54)),X55)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_864])]) ).

fof(c_0_1473,plain,
    ! [X54,X55] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X55))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X54)),X55)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_865])]) ).

fof(c_0_1474,plain,
    ! [X30] : hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),X30))) = hAPP(nat,nat,suc,X30),
    inference(variable_rename,[status(thm)],[c_0_866]) ).

fof(c_0_1475,plain,
    ! [X77,X78,X79,X80] :
      ( ~ hBOOL(hAPP(fun(X78,bool),bool,finite_finite_1(X78),X80))
      | hBOOL(hAPP(fun(X77,bool),bool,finite_finite_1(X77),hAPP(fun(X78,bool),fun(X77,bool),hAPP(fun(X78,X77),fun(fun(X78,bool),fun(X77,bool)),image(X78,X77),X79),X80))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_867])]) ).

fof(c_0_1476,plain,
    ! [X47,X48,X49,X50] :
      ( ( hBOOL(hAPP(fun(X48,bool),bool,hAPP(X48,fun(fun(X48,bool),bool),member(X48),esk69_4(X47,X48,X49,X50)),X50))
        | hBOOL(hAPP(fun(X48,bool),bool,hAPP(fun(X48,X47),fun(fun(X48,bool),bool),inj_on(X48,X47),X49),X50)) )
      & ( hBOOL(hAPP(fun(X48,bool),bool,hAPP(X48,fun(fun(X48,bool),bool),member(X48),esk70_4(X47,X48,X49,X50)),X50))
        | hBOOL(hAPP(fun(X48,bool),bool,hAPP(fun(X48,X47),fun(fun(X48,bool),bool),inj_on(X48,X47),X49),X50)) )
      & ( hAPP(X48,X47,X49,esk69_4(X47,X48,X49,X50)) = hAPP(X48,X47,X49,esk70_4(X47,X48,X49,X50))
        | hBOOL(hAPP(fun(X48,bool),bool,hAPP(fun(X48,X47),fun(fun(X48,bool),bool),inj_on(X48,X47),X49),X50)) )
      & ( ti(X48,esk69_4(X47,X48,X49,X50)) != ti(X48,esk70_4(X47,X48,X49,X50))
        | hBOOL(hAPP(fun(X48,bool),bool,hAPP(fun(X48,X47),fun(fun(X48,bool),bool),inj_on(X48,X47),X49),X50)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_868])])])])]) ).

fof(c_0_1477,plain,
    ! [X54,X55] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),hAPP(nat,nat,suc,X55)))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X55))
      | X54 = hAPP(nat,nat,suc,X55) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_869])]) ).

fof(c_0_1478,plain,
    ! [X55,X56,X57,X58] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X55),hAPP(nat,nat,suc,X56)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X55),X56))
        | X55 = hAPP(nat,nat,suc,X56) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X57),X58))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X57),hAPP(nat,nat,suc,X58))) )
      & ( X57 != hAPP(nat,nat,suc,X58)
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X57),hAPP(nat,nat,suc,X58))) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_870])])])])]) ).

fof(c_0_1479,plain,
    ! [X74,X75] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X74)),X75))
      | X75 = hAPP(nat,nat,suc,esk92_2(X74,X75)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_871])])]) ).

fof(c_0_1480,plain,
    ! [X64,X65,X66] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk86_3(X64,X65,X66)),X66))
        | hBOOL(hAPP(nat,bool,X64,X65))
        | ~ hBOOL(hAPP(nat,bool,X64,X66))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X65),X66)) )
      & ( hBOOL(hAPP(nat,bool,X64,hAPP(nat,nat,suc,esk86_3(X64,X65,X66))))
        | hBOOL(hAPP(nat,bool,X64,X65))
        | ~ hBOOL(hAPP(nat,bool,X64,X66))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X65),X66)) )
      & ( ~ hBOOL(hAPP(nat,bool,X64,esk86_3(X64,X65,X66)))
        | hBOOL(hAPP(nat,bool,X64,X65))
        | ~ hBOOL(hAPP(nat,bool,X64,X66))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X65),X66)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_872])])])]) ).

fof(c_0_1481,plain,
    ! [X8,X9,X10,X11,X12] :
      ( ( hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less_eq(X8),X9),X10))
        | ~ hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less(X8),X9),X10))
        | ~ preorder(X8) )
      & ( ~ hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less_eq(X8),X10),X9))
        | ~ hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less(X8),X9),X10))
        | ~ preorder(X8) )
      & ( ~ hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less_eq(X8),X11),X12))
        | hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less_eq(X8),X12),X11))
        | hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less(X8),X11),X12))
        | ~ preorder(X8) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_873])])])])]) ).

fof(c_0_1482,plain,
    ! [X30] : hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X30))) = X30,
    inference(variable_rename,[status(thm)],[c_0_874]) ).

fof(c_0_1483,plain,
    ! [X65,X66,X68,X69,X70] :
      ( ( X65 = hAPP(nat,nat,suc,esk85_2(X65,X66))
        | X65 = zero_zero(nat)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X65),hAPP(nat,nat,suc,X66))) )
      & ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk85_2(X65,X66)),X66))
        | X65 = zero_zero(nat)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X65),hAPP(nat,nat,suc,X66))) )
      & ( X68 != zero_zero(nat)
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X68),hAPP(nat,nat,suc,X69))) )
      & ( X68 != hAPP(nat,nat,suc,X70)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X70),X69))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X68),hAPP(nat,nat,suc,X69))) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_875])])])])])]) ).

fof(c_0_1484,plain,
    ! [X44,X45,X46] :
      ( ( hBOOL(hAPP(fun(X44,bool),bool,hAPP(X44,fun(fun(X44,bool),bool),member(X44),esk53_3(X44,X45,X46)),X46))
        | hBOOL(hAPP(fun(X44,bool),bool,hAPP(fun(X44,bool),fun(fun(X44,bool),bool),ord_less_eq(fun(X44,bool)),X46),X45)) )
      & ( ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(X44,fun(fun(X44,bool),bool),member(X44),esk53_3(X44,X45,X46)),X45))
        | hBOOL(hAPP(fun(X44,bool),bool,hAPP(fun(X44,bool),fun(fun(X44,bool),bool),ord_less_eq(fun(X44,bool)),X46),X45)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_876])])])]) ).

fof(c_0_1485,plain,
    ! [X38,X39] :
      ( ~ hBOOL(hAPP(fun(X38,bool),bool,finite_finite_1(X38),top_top(fun(X38,bool))))
      | ~ hBOOL(hAPP(fun(X38,bool),bool,hAPP(fun(X38,X38),fun(fun(X38,bool),bool),inj_on(X38,X38),X39),top_top(fun(X38,bool))))
      | hAPP(fun(X38,bool),fun(X38,bool),hAPP(fun(X38,X38),fun(fun(X38,bool),fun(X38,bool)),image(X38,X38),X39),top_top(fun(X38,bool))) = top_top(fun(X38,bool)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_877])])])]) ).

fof(c_0_1486,plain,
    ! [X54,X55] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),hAPP(nat,nat,suc,X55)))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X55))
      | X54 = X55 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_878])]) ).

fof(c_0_1487,plain,
    ! [X54,X55] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X55))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),hAPP(nat,nat,suc,X55)))
      | X55 = X54 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_879])]) ).

fof(c_0_1488,plain,
    ! [X55,X56] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X55),hAPP(nat,nat,suc,X56)))
        | X55 = X56
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X55),X56)) )
      & ( X55 != X56
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X55),hAPP(nat,nat,suc,X56)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X55),X56)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_880])])]) ).

fof(c_0_1489,plain,
    ! [X55,X56,X57,X58] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X55),hAPP(nat,nat,suc,X56)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X55),X56))
        | X55 = X56 )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X57),X58))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X57),hAPP(nat,nat,suc,X58))) )
      & ( X57 != X58
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X57),hAPP(nat,nat,suc,X58))) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_881])])])])]) ).

fof(c_0_1490,plain,
    ! [X55,X56,X57,X58] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X55),hAPP(nat,nat,suc,X56)))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X55),X56)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X57),X58))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X57),hAPP(nat,nat,suc,X58))) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_882])])])]) ).

fof(c_0_1491,plain,
    ! [X54] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X54)),X54)),
    inference(variable_rename,[status(thm)],[c_0_883]) ).

fof(c_0_1492,plain,
    ! [X44,X45,X46,X47,X48,X49] :
      ( ( ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(fun(X44,bool),fun(fun(X44,bool),bool),ord_less_eq(fun(X44,bool)),X45),X46))
        | hBOOL(hAPP(fun(X44,bool),bool,hAPP(fun(X44,bool),fun(fun(X44,bool),bool),ord_less(fun(X44,bool)),X45),X46))
        | ti(fun(X44,bool),X45) = ti(fun(X44,bool),X46) )
      & ( ~ hBOOL(hAPP(fun(X47,bool),bool,hAPP(fun(X47,bool),fun(fun(X47,bool),bool),ord_less(fun(X47,bool)),X48),X49))
        | hBOOL(hAPP(fun(X47,bool),bool,hAPP(fun(X47,bool),fun(fun(X47,bool),bool),ord_less_eq(fun(X47,bool)),X48),X49)) )
      & ( ti(fun(X47,bool),X48) != ti(fun(X47,bool),X49)
        | hBOOL(hAPP(fun(X47,bool),bool,hAPP(fun(X47,bool),fun(fun(X47,bool),bool),ord_less_eq(fun(X47,bool)),X48),X49)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_884])])])])]) ).

fof(c_0_1493,plain,
    ! [X44,X45,X46,X47,X48,X49] :
      ( ( hBOOL(hAPP(fun(X44,bool),bool,hAPP(fun(X44,bool),fun(fun(X44,bool),bool),ord_less_eq(fun(X44,bool)),X45),X46))
        | ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(fun(X44,bool),fun(fun(X44,bool),bool),ord_less(fun(X44,bool)),X45),X46)) )
      & ( ti(fun(X44,bool),X45) != ti(fun(X44,bool),X46)
        | ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(fun(X44,bool),fun(fun(X44,bool),bool),ord_less(fun(X44,bool)),X45),X46)) )
      & ( ~ hBOOL(hAPP(fun(X47,bool),bool,hAPP(fun(X47,bool),fun(fun(X47,bool),bool),ord_less_eq(fun(X47,bool)),X48),X49))
        | ti(fun(X47,bool),X48) = ti(fun(X47,bool),X49)
        | hBOOL(hAPP(fun(X47,bool),bool,hAPP(fun(X47,bool),fun(fun(X47,bool),bool),ord_less(fun(X47,bool)),X48),X49)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_885])])])])]) ).

fof(c_0_1494,plain,
    ! [X44,X45,X46] :
      ( ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(fun(X44,bool),fun(fun(X44,bool),bool),ord_less(fun(X44,bool)),X45),X46))
      | hBOOL(hAPP(fun(X44,bool),bool,hAPP(fun(X44,bool),fun(fun(X44,bool),bool),ord_less_eq(fun(X44,bool)),X45),X46)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_886])]) ).

fof(c_0_1495,plain,
    ! [X61,X63,X64,X65] :
      ( ( ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X61))
        | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X63),X61))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X63),esk75_1(X61))) )
      & ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),esk76_2(X64,X65)),X64))
        | hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X64)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk76_2(X64,X65)),X65))
        | hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X64)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_887])])])])])]) ).

fof(c_0_1496,plain,
    ! [X61,X63,X64,X65] :
      ( ( ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X61))
        | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X63),X61))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X63),esk73_1(X61))) )
      & ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),esk74_2(X64,X65)),X64))
        | hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X64)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),esk74_2(X64,X65)),X65))
        | hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X64)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_888])])])])])]) ).

fof(c_0_1497,plain,
    ! [X63,X64,X66] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk79_2(X63,X64)),X63))
        | ~ hBOOL(hAPP(nat,bool,X64,X63))
        | hBOOL(hAPP(nat,bool,X64,zero_zero(nat))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X66),esk79_2(X63,X64)))
        | ~ hBOOL(hAPP(nat,bool,X64,X66))
        | ~ hBOOL(hAPP(nat,bool,X64,X63))
        | hBOOL(hAPP(nat,bool,X64,zero_zero(nat))) )
      & ( hBOOL(hAPP(nat,bool,X64,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),esk79_2(X63,X64)),one_one(nat))))
        | ~ hBOOL(hAPP(nat,bool,X64,X63))
        | hBOOL(hAPP(nat,bool,X64,zero_zero(nat))) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_889])])])])]) ).

fof(c_0_1498,plain,
    ! [X8,X9,X10] :
      ( ( hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less(X8),X9),X10))
        | ti(X8,X9) = ti(X8,X10)
        | ~ hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less_eq(X8),X9),X10))
        | ~ linorder(X8) )
      & ( ti(X8,X9) != ti(X8,X10)
        | ~ hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less(X8),X9),X10))
        | ~ hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less_eq(X8),X9),X10))
        | ~ linorder(X8) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_890])])])]) ).

fof(c_0_1499,plain,
    ! [X8,X9,X10,X11,X12] :
      ( ( hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less_eq(X8),X9),X10))
        | ti(X8,X9) != ti(X8,X10)
        | ~ order(X8) )
      & ( hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less_eq(X8),X10),X9))
        | ti(X8,X9) != ti(X8,X10)
        | ~ order(X8) )
      & ( ~ hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less_eq(X8),X11),X12))
        | ~ hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less_eq(X8),X12),X11))
        | ti(X8,X11) = ti(X8,X12)
        | ~ order(X8) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_891])])])])]) ).

fof(c_0_1500,plain,
    ! [X8,X9,X10] :
      ( ( ~ hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less_eq(X8),X10),X9))
        | ti(X8,X10) = ti(X8,X9)
        | ~ hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less_eq(X8),X9),X10))
        | ~ order(X8) )
      & ( ti(X8,X10) != ti(X8,X9)
        | hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less_eq(X8),X10),X9))
        | ~ hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less_eq(X8),X9),X10))
        | ~ order(X8) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_892])])])]) ).

fof(c_0_1501,plain,
    ! [X35,X36,X37] :
      ( ~ order(X35)
      | ~ hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less_eq(X35),X36),X37))
      | ~ hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less_eq(X35),X37),X36))
      | ti(X35,X36) = ti(X35,X37) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_893])])]) ).

fof(c_0_1502,plain,
    ! [X35,X36,X37] :
      ( ~ order(X35)
      | ~ hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less_eq(X35),X36),X37))
      | ~ hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less_eq(X35),X37),X36))
      | ti(X35,X37) = ti(X35,X36) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_894])])]) ).

fof(c_0_1503,plain,
    ! [X38,X39] :
      ( ~ hBOOL(hAPP(fun(X38,bool),bool,finite_finite_1(X38),top_top(fun(X38,bool))))
      | hAPP(fun(X38,bool),fun(X38,bool),hAPP(fun(X38,X38),fun(fun(X38,bool),fun(X38,bool)),image(X38,X38),X39),top_top(fun(X38,bool))) != top_top(fun(X38,bool))
      | hBOOL(hAPP(fun(X38,bool),bool,hAPP(fun(X38,X38),fun(fun(X38,bool),bool),inj_on(X38,X38),X39),top_top(fun(X38,bool)))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_895])])])]) ).

fof(c_0_1504,plain,
    ! [X12,X13,X14,X15] :
      ( ~ preorder(X12)
      | ~ hBOOL(hAPP(X12,bool,hAPP(X12,fun(X12,bool),ord_less(X12),X14),X15))
      | ~ hBOOL(hAPP(X12,bool,hAPP(X12,fun(X12,bool),ord_less(X12),X15),X14))
      | hBOOL(X13) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_896])])]) ).

fof(c_0_1505,plain,
    ! [X35,X36,X37] :
      ( ~ linorder(X35)
      | ~ hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less_eq(X35),X36),X37))
      | ~ hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less(X35),X37),X36)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_897])])]) ).

fof(c_0_1506,plain,
    ! [X8,X9,X10,X11,X12] :
      ( ( hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less_eq(X8),X9),X10))
        | hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less(X8),X10),X9))
        | ~ linorder(X8) )
      & ( ~ hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less(X8),X12),X11))
        | ~ hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less_eq(X8),X11),X12))
        | ~ linorder(X8) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_898])])])])]) ).

fof(c_0_1507,plain,
    ! [X8,X9,X10,X11,X12] :
      ( ( hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less(X8),X9),X10))
        | hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less_eq(X8),X10),X9))
        | ~ linorder(X8) )
      & ( ~ hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less_eq(X8),X12),X11))
        | ~ hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less(X8),X11),X12))
        | ~ linorder(X8) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_899])])])])]) ).

fof(c_0_1508,plain,
    ! [X8,X9,X10,X11,X12] :
      ( ( hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less(X8),X9),X10))
        | hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less(X8),X10),X9))
        | ti(X8,X9) = ti(X8,X10)
        | ~ linorder(X8) )
      & ( ~ hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less(X8),X12),X11))
        | ~ hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less(X8),X11),X12))
        | ~ linorder(X8) )
      & ( ti(X8,X11) != ti(X8,X12)
        | ~ hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less(X8),X11),X12))
        | ~ linorder(X8) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_900])])])])]) ).

fof(c_0_1509,plain,
    ! [X35,X36,X37] :
      ( ~ preorder(X35)
      | ~ hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less(X35),X36),X37))
      | ~ hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less(X35),X37),X36)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_901])])]) ).

fof(c_0_1510,plain,
    ! [X35,X36,X37] :
      ( ~ preorder(X35)
      | ~ hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less(X35),X36),X37))
      | ~ hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less(X35),X37),X36)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_902])])]) ).

fof(c_0_1511,plain,
    ! [X23,X24,X25] :
      ( ~ preorder(X23)
      | ~ hBOOL(hAPP(X23,bool,hAPP(X23,fun(X23,bool),ord_less(X23),X24),X25))
      | ~ hBOOL(hAPP(X23,bool,hAPP(X23,fun(X23,bool),ord_less(X23),X25),X24)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_903])])]) ).

fof(c_0_1512,plain,
    ! [X23,X24,X25] :
      ( ~ order(X23)
      | ~ hBOOL(hAPP(X23,bool,hAPP(X23,fun(X23,bool),ord_less(X23),X24),X25))
      | ~ hBOOL(hAPP(X23,bool,hAPP(X23,fun(X23,bool),ord_less(X23),X25),X24)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_904])])]) ).

fof(c_0_1513,plain,
    ! [X35,X36,X37] :
      ( ~ preorder(X35)
      | ~ hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less(X35),X36),X37))
      | ~ hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less(X35),X37),X36)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_905])])]) ).

fof(c_0_1514,plain,
    ! [X54,X55] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X55))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),hAPP(nat,nat,suc,X55))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_906])]) ).

fof(c_0_1515,plain,
    ! [X54,X55] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X55))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),hAPP(nat,nat,suc,X55))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_907])]) ).

fof(c_0_1516,plain,
    ! [X54,X55] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X55))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),hAPP(nat,nat,suc,X55))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_908])]) ).

fof(c_0_1517,plain,
    ! [X4] :
      ( ~ linordered_semidom(X4)
      | hBOOL(hAPP(X4,bool,hAPP(X4,fun(X4,bool),ord_less(X4),zero_zero(X4)),hAPP(X4,X4,hAPP(X4,fun(X4,X4),plus_plus(X4),one_one(X4)),one_one(X4)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_909])]) ).

fof(c_0_1518,plain,
    ! [X54,X55] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X55))
      | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X55),X54))
      | X54 = X55 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_910])]) ).

fof(c_0_1519,plain,
    ! [X22,X23] :
      ( ~ linordered_semidom(X22)
      | hBOOL(hAPP(X22,bool,hAPP(X22,fun(X22,bool),ord_less(X22),X23),hAPP(X22,X22,hAPP(X22,fun(X22,X22),plus_plus(X22),X23),one_one(X22)))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_911])])]) ).

fof(c_0_1520,plain,
    ! [X46,X47,X48,X49] :
      ( ~ comm_semiring_1(X46)
      | hAPP(X46,X46,hAPP(X46,fun(X46,X46),plus_plus(X46),X47),hAPP(X46,X46,hAPP(X46,fun(X46,X46),plus_plus(X46),X48),X49)) = hAPP(X46,X46,hAPP(X46,fun(X46,X46),plus_plus(X46),X48),hAPP(X46,X46,hAPP(X46,fun(X46,X46),plus_plus(X46),X47),X49)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_912])])]) ).

fof(c_0_1521,plain,
    ! [X36,X37,X38] :
      ( ( hBOOL(hAPP(X36,bool,hAPP(X36,fun(X36,bool),ord_less(X36),esk37_3(X36,X37,X38)),X38))
        | hBOOL(hAPP(X36,bool,hAPP(X36,fun(X36,bool),ord_less_eq(X36),X38),X37))
        | ~ dense_linorder(X36) )
      & ( ~ hBOOL(hAPP(X36,bool,hAPP(X36,fun(X36,bool),ord_less_eq(X36),esk37_3(X36,X37,X38)),X37))
        | hBOOL(hAPP(X36,bool,hAPP(X36,fun(X36,bool),ord_less_eq(X36),X38),X37))
        | ~ dense_linorder(X36) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_913])])])])]) ).

fof(c_0_1522,plain,
    ! [X40,X41] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X40,bool),nat,finite_card(X40),X41)))
      | hBOOL(hAPP(fun(X40,bool),bool,finite_finite_1(X40),X41)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_914])]) ).

fof(c_0_1523,plain,
    ! [X44,X45,X46] :
      ( ~ hBOOL(hAPP(fun(X44,bool),bool,finite_finite_1(X44),X46))
      | ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(fun(X44,bool),fun(fun(X44,bool),bool),ord_less_eq(fun(X44,bool)),X45),X46))
      | hBOOL(hAPP(fun(X44,bool),bool,finite_finite_1(X44),X45)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_915])]) ).

fof(c_0_1524,plain,
    ! [X44,X45,X46] :
      ( ~ hBOOL(hAPP(fun(X44,bool),bool,hAPP(fun(X44,bool),fun(fun(X44,bool),bool),ord_less_eq(fun(X44,bool)),X45),X46))
      | ~ hBOOL(hAPP(fun(X44,bool),bool,finite_finite_1(X44),X46))
      | hBOOL(hAPP(fun(X44,bool),bool,finite_finite_1(X44),X45)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_916])]) ).

fof(c_0_1525,plain,
    ! [X54,X55] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),X55))),
    inference(variable_rename,[status(thm)],[c_0_917]) ).

fof(c_0_1526,plain,
    ! [X54,X55] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X55),X54))),
    inference(variable_rename,[status(thm)],[c_0_918]) ).

fof(c_0_1527,plain,
    ! [X36,X37,X38] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X36),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X37),X38)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X37),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X36),X38)),
    inference(variable_rename,[status(thm)],[c_0_919]) ).

fof(c_0_1528,plain,
    ! [X63,X64,X66] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),esk81_2(X63,X64)),X63))
        | ~ hBOOL(hAPP(nat,bool,X64,X63))
        | hBOOL(hAPP(nat,bool,X64,zero_zero(nat))) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X66),esk81_2(X63,X64)))
        | ~ hBOOL(hAPP(nat,bool,X64,X66))
        | ~ hBOOL(hAPP(nat,bool,X64,X63))
        | hBOOL(hAPP(nat,bool,X64,zero_zero(nat))) )
      & ( hBOOL(hAPP(nat,bool,X64,esk81_2(X63,X64)))
        | ~ hBOOL(hAPP(nat,bool,X64,X63))
        | hBOOL(hAPP(nat,bool,X64,zero_zero(nat))) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_920])])])])]) ).

fof(c_0_1529,plain,
    ! [X51,X52,X53,X54] :
      ( ~ hBOOL(hAPP(X51,bool,X53,X54))
      | ~ hBOOL(hAPP(fun(X51,bool),bool,hAPP(fun(X51,bool),fun(fun(X51,bool),bool),ord_less_eq(fun(X51,bool)),X53),X52))
      | hBOOL(hAPP(X51,bool,X52,X54)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_921])]) ).

fof(c_0_1530,plain,
    ! [X51,X52,X53,X54] :
      ( ~ hBOOL(hAPP(fun(X51,bool),bool,hAPP(fun(X51,bool),fun(fun(X51,bool),bool),ord_less_eq(fun(X51,bool)),X53),X54))
      | ~ hBOOL(hAPP(X51,bool,X53,X52))
      | hBOOL(hAPP(X51,bool,X54,X52)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_922])]) ).

fof(c_0_1531,plain,
    ! [X40,X41] :
      ( hBOOL(hAPP(fun(X40,bool),bool,finite_finite_1(X40),top_top(fun(X40,bool))))
      | ~ hBOOL(hAPP(fun(X40,bool),bool,finite_finite_1(X40),X41))
      | ~ hBOOL(hAPP(fun(X40,bool),bool,hAPP(X40,fun(fun(X40,bool),bool),member(X40),esk72_2(X40,X41)),X41)) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_923])])])])]) ).

fof(c_0_1532,plain,
    ! [X63,X64,X66,X67,X68] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X63),X64))
        | X64 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X63),esk83_2(X63,X64))) )
      & ( X67 != hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X66),X68))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X66),X67)) ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_924])])])])]) ).

fof(c_0_1533,plain,
    ! [X89,X90,X91,X92,X93,X94] : hAPP(X89,X90,hAPP(fun(X89,X91),fun(X89,X90),hAPP(fun(X89,fun(X91,X90)),fun(fun(X89,X91),fun(X89,X90)),combs(X89,X91,X90),X92),X93),X94) = hAPP(X91,X90,hAPP(X89,fun(X91,X90),X92,X94),hAPP(X89,X91,X93,X94)),
    inference(variable_rename,[status(thm)],[c_0_925]) ).

fof(c_0_1534,plain,
    ! [X65,X66] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X65),esk93_2(X65,X66)))
        | X66 = hAPP(nat,nat,suc,X65)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X65),X66)) )
      & ( X66 = hAPP(nat,nat,suc,esk93_2(X65,X66))
        | X66 = hAPP(nat,nat,suc,X65)
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X65),X66)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_926])])])]) ).

fof(c_0_1535,plain,
    ! [X63,X64] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X63),X64))
      | X64 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X63),esk87_2(X63,X64))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_927])])]) ).

fof(c_0_1536,plain,
    ! [X15,X16] :
      ( ( hAPP(X15,X15,hAPP(X15,fun(X15,X15),plus_plus(X15),X16),X16) != zero_zero(X15)
        | ti(X15,X16) = zero_zero(X15)
        | ~ hBOOL(hAPP(fun(X15,bool),bool,hAPP(X15,fun(fun(X15,bool),bool),member(X15),X16),ring_1_Ints(X15)))
        | ~ ring_char_0(X15) )
      & ( ti(X15,X16) != zero_zero(X15)
        | hAPP(X15,X15,hAPP(X15,fun(X15,X15),plus_plus(X15),X16),X16) = zero_zero(X15)
        | ~ hBOOL(hAPP(fun(X15,bool),bool,hAPP(X15,fun(fun(X15,bool),bool),member(X15),X16),ring_1_Ints(X15)))
        | ~ ring_char_0(X15) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_928])])])]) ).

fof(c_0_1537,plain,
    ! [X37,X38,X39,X40] :
      ( ~ order(X37)
      | ti(X37,X39) != ti(X37,X40)
      | ~ hBOOL(hAPP(X37,bool,hAPP(X37,fun(X37,bool),ord_less_eq(X37),X38),X40))
      | hBOOL(hAPP(X37,bool,hAPP(X37,fun(X37,bool),ord_less_eq(X37),X38),X39)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_929])])]) ).

fof(c_0_1538,plain,
    ! [X37,X38,X39,X40] :
      ( ~ order(X37)
      | ~ hBOOL(hAPP(X37,bool,hAPP(X37,fun(X37,bool),ord_less_eq(X37),X39),X40))
      | ti(X37,X39) != ti(X37,X38)
      | hBOOL(hAPP(X37,bool,hAPP(X37,fun(X37,bool),ord_less_eq(X37),X38),X40)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_930])])]) ).

fof(c_0_1539,plain,
    ! [X8,X9,X10] :
      ( ( hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less(X8),X10),X9))
        | ti(X8,X10) = ti(X8,X9)
        | hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less(X8),X9),X10))
        | ~ linorder(X8) )
      & ( ti(X8,X10) != ti(X8,X9)
        | ~ hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less(X8),X10),X9))
        | hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less(X8),X9),X10))
        | ~ linorder(X8) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_931])])])]) ).

fof(c_0_1540,plain,
    ! [X37,X38,X39,X40] :
      ( ~ order(X37)
      | ti(X37,X39) != ti(X37,X40)
      | ~ hBOOL(hAPP(X37,bool,hAPP(X37,fun(X37,bool),ord_less(X37),X38),X40))
      | hBOOL(hAPP(X37,bool,hAPP(X37,fun(X37,bool),ord_less(X37),X38),X39)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_932])])]) ).

fof(c_0_1541,plain,
    ! [X37,X38,X39,X40] :
      ( ~ order(X37)
      | ~ hBOOL(hAPP(X37,bool,hAPP(X37,fun(X37,bool),ord_less(X37),X39),X40))
      | ti(X37,X39) != ti(X37,X38)
      | hBOOL(hAPP(X37,bool,hAPP(X37,fun(X37,bool),ord_less(X37),X38),X40)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_933])])]) ).

fof(c_0_1542,plain,
    ! [X23,X24,X25] :
      ( ~ order(X23)
      | ~ hBOOL(hAPP(X23,bool,hAPP(X23,fun(X23,bool),ord_less_eq(X23),X24),X25))
      | ti(X23,X25) = ti(X23,X24)
      | hBOOL(hAPP(X23,bool,hAPP(X23,fun(X23,bool),ord_less(X23),X24),X25)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_934])])]) ).

fof(c_0_1543,plain,
    ! [X23,X24,X25] :
      ( ~ order(X23)
      | ~ hBOOL(hAPP(X23,bool,hAPP(X23,fun(X23,bool),ord_less_eq(X23),X24),X25))
      | ti(X23,X24) = ti(X23,X25)
      | hBOOL(hAPP(X23,bool,hAPP(X23,fun(X23,bool),ord_less(X23),X24),X25)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_935])])]) ).

fof(c_0_1544,plain,
    ! [X35,X36,X37] :
      ( ~ order(X35)
      | ~ hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less_eq(X35),X36),X37))
      | hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less(X35),X36),X37))
      | ti(X35,X36) = ti(X35,X37) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_936])])]) ).

fof(c_0_1545,plain,
    ! [X23,X24,X25] :
      ( ~ order(X23)
      | ti(X23,X24) = ti(X23,X25)
      | ~ hBOOL(hAPP(X23,bool,hAPP(X23,fun(X23,bool),ord_less_eq(X23),X25),X24))
      | hBOOL(hAPP(X23,bool,hAPP(X23,fun(X23,bool),ord_less(X23),X25),X24)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_937])])]) ).

fof(c_0_1546,plain,
    ! [X23,X24,X25] :
      ( ~ order(X23)
      | ti(X23,X24) = ti(X23,X25)
      | ~ hBOOL(hAPP(X23,bool,hAPP(X23,fun(X23,bool),ord_less_eq(X23),X24),X25))
      | hBOOL(hAPP(X23,bool,hAPP(X23,fun(X23,bool),ord_less(X23),X24),X25)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_938])])]) ).

fof(c_0_1547,plain,
    ! [X8,X9,X10] :
      ( ( ~ hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less_eq(X8),X9),X10))
        | ti(X8,X9) = ti(X8,X10)
        | hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less(X8),X9),X10))
        | ~ linorder(X8) )
      & ( ti(X8,X9) != ti(X8,X10)
        | hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less_eq(X8),X9),X10))
        | hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less(X8),X9),X10))
        | ~ linorder(X8) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_939])])])]) ).

fof(c_0_1548,plain,
    ! [X8,X9,X10,X11,X12] :
      ( ( ~ hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less_eq(X8),X9),X10))
        | hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less(X8),X9),X10))
        | ti(X8,X9) = ti(X8,X10)
        | ~ order(X8) )
      & ( ~ hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less(X8),X11),X12))
        | hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less_eq(X8),X11),X12))
        | ~ order(X8) )
      & ( ti(X8,X11) != ti(X8,X12)
        | hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less_eq(X8),X11),X12))
        | ~ order(X8) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_940])])])])]) ).

fof(c_0_1549,plain,
    ! [X8,X9,X10,X11,X12] :
      ( ( hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less_eq(X8),X9),X10))
        | ~ hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less(X8),X9),X10))
        | ~ order(X8) )
      & ( ti(X8,X9) != ti(X8,X10)
        | ~ hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less(X8),X9),X10))
        | ~ order(X8) )
      & ( ~ hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less_eq(X8),X11),X12))
        | ti(X8,X11) = ti(X8,X12)
        | hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less(X8),X11),X12))
        | ~ order(X8) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_941])])])])]) ).

fof(c_0_1550,plain,
    ! [X38,X39,X40,X41,X42] :
      ( ~ hBOOL(hAPP(fun(X38,bool),bool,hAPP(fun(X38,X39),fun(fun(X38,bool),bool),inj_on(X38,X39),X42),top_top(fun(X38,bool))))
      | hAPP(X38,X39,X42,X40) != hAPP(X38,X39,X42,X41)
      | ti(X38,X40) = ti(X38,X41) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_942])]) ).

fof(c_0_1551,plain,
    ! [X38,X39,X40,X41,X42] :
      ( ( hAPP(X38,X39,X42,X40) != hAPP(X38,X39,X42,X41)
        | ti(X38,X40) = ti(X38,X41)
        | ~ hBOOL(hAPP(fun(X38,bool),bool,hAPP(fun(X38,X39),fun(fun(X38,bool),bool),inj_on(X38,X39),X42),top_top(fun(X38,bool)))) )
      & ( ti(X38,X40) != ti(X38,X41)
        | hAPP(X38,X39,X42,X40) = hAPP(X38,X39,X42,X41)
        | ~ hBOOL(hAPP(fun(X38,bool),bool,hAPP(fun(X38,X39),fun(fun(X38,bool),bool),inj_on(X38,X39),X42),top_top(fun(X38,bool)))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_943])])]) ).

fof(c_0_1552,plain,
    ! [X37,X38,X39,X40] :
      ( ~ ord(X37)
      | X39 != X40
      | ~ hBOOL(hAPP(X37,bool,hAPP(X37,fun(X37,bool),ord_less_eq(X37),X40),X38))
      | hBOOL(hAPP(X37,bool,hAPP(X37,fun(X37,bool),ord_less_eq(X37),X39),X38)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_944])])]) ).

fof(c_0_1553,plain,
    ! [X37,X38,X39,X40] :
      ( ~ ord(X37)
      | ~ hBOOL(hAPP(X37,bool,hAPP(X37,fun(X37,bool),ord_less_eq(X37),X39),X40))
      | X40 != X38
      | hBOOL(hAPP(X37,bool,hAPP(X37,fun(X37,bool),ord_less_eq(X37),X39),X38)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_945])])]) ).

fof(c_0_1554,plain,
    ! [X37,X38,X39,X40] :
      ( ~ ord(X37)
      | X39 != X40
      | ~ hBOOL(hAPP(X37,bool,hAPP(X37,fun(X37,bool),ord_less(X37),X40),X38))
      | hBOOL(hAPP(X37,bool,hAPP(X37,fun(X37,bool),ord_less(X37),X39),X38)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_946])])]) ).

fof(c_0_1555,plain,
    ! [X37,X38,X39,X40] :
      ( ~ ord(X37)
      | ~ hBOOL(hAPP(X37,bool,hAPP(X37,fun(X37,bool),ord_less(X37),X39),X40))
      | X40 != X38
      | hBOOL(hAPP(X37,bool,hAPP(X37,fun(X37,bool),ord_less(X37),X39),X38)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_947])])]) ).

fof(c_0_1556,plain,
    ! [X35,X36,X37] :
      ( ~ preorder(X35)
      | ~ hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less(X35),X36),X37))
      | hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less_eq(X35),X36),X37)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_948])])]) ).

fof(c_0_1557,plain,
    ! [X78,X79] : hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X78),X79))),
    inference(variable_rename,[status(thm)],[c_0_949]) ).

fof(c_0_1558,plain,
    ! [X63,X64] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),esk82_2(X63,X64)))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X63),X64)) )
      & ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X63),esk82_2(X63,X64)) = X64
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X63),X64)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_950])])])]) ).

fof(c_0_1559,plain,
    ! [X29,X30,X31,X32,X33,X34] : hAPP(product_prod(X29,X30),X31,hAPP(fun(X29,fun(X30,X31)),fun(product_prod(X29,X30),X31),product_prod_rec(X29,X30,X31),X32),hAPP(X30,product_prod(X29,X30),hAPP(X29,fun(X30,product_prod(X29,X30)),product_Pair(X29,X30),X33),X34)) = hAPP(X30,X31,hAPP(X29,fun(X30,X31),X32,X33),X34),
    inference(variable_rename,[status(thm)],[c_0_951]) ).

fof(c_0_1560,plain,
    ! [X54,X55] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X55))
      | X54 = X55
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X55)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_952])]) ).

fof(c_0_1561,plain,
    ! [X55,X56,X57,X58] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X55),X56))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X55),X56))
        | X55 = X56 )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X57),X58))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X57),X58)) )
      & ( X57 != X58
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X57),X58)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_953])])])])]) ).

fof(c_0_1562,plain,
    ! [X55,X56,X57,X58] :
      ( ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X55),X56))
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X55),X56)) )
      & ( X55 != X56
        | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X55),X56)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X57),X58))
        | X57 = X58
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X57),X58)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_954])])])])]) ).

fof(c_0_1563,plain,
    ! [X35,X36] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X35),X36))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X35),X36)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_955])]) ).

fof(c_0_1564,plain,
    ! [X54,X55] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X55))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X55)) )
      & ( X54 != X55
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X55)) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_956])])]) ).

fof(c_0_1565,plain,
    ! [X54,X55] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X55))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X55)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_957])]) ).

fof(c_0_1566,plain,
    ! [X30,X31] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X30),hAPP(nat,nat,suc,zero_zero(nat))))
        | X30 = zero_zero(nat) )
      & ( X31 != zero_zero(nat)
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X31),hAPP(nat,nat,suc,zero_zero(nat)))) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_958])])])]) ).

fof(c_0_1567,plain,
    ! [X4] :
      ( ~ hBOOL(hAPP(fun(X4,bool),bool,finite_finite_1(X4),top_top(fun(X4,bool))))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X4,bool),nat,finite_card(X4),top_top(fun(X4,bool))))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_959])]) ).

fof(c_0_1568,plain,
    hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),esk66_0),arrow_2064824852le_Lin)),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_960])]) ).

fof(c_0_1569,axiom,
    hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),lba),arrow_2064824852le_Lin)),
    c_0_961 ).

fof(c_0_1570,axiom,
    hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),lab),arrow_2064824852le_Lin)),
    c_0_962 ).

fof(c_0_1571,plain,
    ! [X45,X46] :
      ( ( hBOOL(hAPP(nat,bool,X46,esk98_2(X45,X46)))
        | hBOOL(hAPP(nat,bool,X46,X45))
        | ~ hBOOL(hAPP(nat,bool,X46,zero_zero(nat))) )
      & ( ~ hBOOL(hAPP(nat,bool,X46,hAPP(nat,nat,suc,esk98_2(X45,X46))))
        | hBOOL(hAPP(nat,bool,X46,X45))
        | ~ hBOOL(hAPP(nat,bool,X46,zero_zero(nat))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_963])])])]) ).

fof(c_0_1572,plain,
    ! [X89,X90,X91,X92,X93,X94] : hAPP(X89,X90,hAPP(X91,fun(X89,X90),hAPP(fun(X89,fun(X91,X90)),fun(X91,fun(X89,X90)),combc(X89,X91,X90),X92),X93),X94) = hAPP(X91,X90,hAPP(X89,fun(X91,X90),X92,X94),X93),
    inference(variable_rename,[status(thm)],[c_0_964]) ).

fof(c_0_1573,plain,
    ! [X89,X90,X91,X92,X93,X94] : hAPP(X89,X90,hAPP(fun(X89,X91),fun(X89,X90),hAPP(fun(X91,X90),fun(fun(X89,X91),fun(X89,X90)),combb(X91,X90,X89),X92),X93),X94) = hAPP(X91,X90,X92,hAPP(X89,X91,X93,X94)),
    inference(variable_rename,[status(thm)],[c_0_965]) ).

fof(c_0_1574,plain,
    ! [X54,X55] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,X54)),X55) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),X55)),
    inference(variable_rename,[status(thm)],[c_0_966]) ).

fof(c_0_1575,plain,
    ! [X40,X41,X42,X43,X44,X45] :
      ( ( ~ hBOOL(hAPP(fun(X40,bool),bool,hAPP(X40,fun(fun(X40,bool),bool),member(X40),X41),X42))
        | hBOOL(hAPP(X40,bool,X42,X41)) )
      & ( ~ hBOOL(hAPP(X43,bool,X45,X44))
        | hBOOL(hAPP(fun(X43,bool),bool,hAPP(X43,fun(fun(X43,bool),bool),member(X43),X44),X45)) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_967])])])]) ).

fof(c_0_1576,plain,
    ! [X63,X64,X66,X67,X68] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X63),X64))
        | X64 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X63),esk60_2(X63,X64)) )
      & ( X67 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X66),X68)
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X66),X67)) ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_968])])])])]) ).

fof(c_0_1577,plain,
    ! [X35,X36,X37] :
      ( ~ linordered_idom(X35)
      | ti(X35,X36) = ti(X35,X37)
      | hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less(X35),X36),X37))
      | hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less(X35),X37),X36)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_969])])]) ).

fof(c_0_1578,plain,
    ! [X8,X9,X10,X11,X12] :
      ( ( ti(X8,X9) = ti(X8,X10)
        | hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less(X8),X9),X10))
        | hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less(X8),X10),X9))
        | ~ linorder(X8) )
      & ( ~ hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less(X8),X11),X12))
        | ti(X8,X11) != ti(X8,X12)
        | ~ linorder(X8) )
      & ( ~ hBOOL(hAPP(X8,bool,hAPP(X8,fun(X8,bool),ord_less(X8),X12),X11))
        | ti(X8,X11) != ti(X8,X12)
        | ~ linorder(X8) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_970])])])])]) ).

fof(c_0_1579,plain,
    ! [X35,X36,X37] :
      ( ~ linorder(X35)
      | hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less(X35),X36),X37))
      | ti(X35,X36) = ti(X35,X37)
      | hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less(X35),X37),X36)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_971])])]) ).

fof(c_0_1580,plain,
    ! [X35,X36,X37] :
      ( ~ linorder(X35)
      | ti(X35,X36) = ti(X35,X37)
      | hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less(X35),X36),X37))
      | hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less(X35),X37),X36)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_972])])]) ).

fof(c_0_1581,plain,
    ! [X35,X36,X37] :
      ( ~ linorder(X35)
      | hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less(X35),X36),X37))
      | ti(X35,X36) = ti(X35,X37)
      | hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less(X35),X37),X36)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_973])])]) ).

fof(c_0_1582,plain,
    ! [X35,X36,X37] :
      ( ~ linorder(X35)
      | hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less_eq(X35),X36),X37))
      | hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less(X35),X37),X36)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_974])])]) ).

fof(c_0_1583,plain,
    ! [X35,X36,X37] :
      ( ~ linorder(X35)
      | hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less(X35),X36),X37))
      | hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less_eq(X35),X37),X36)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_975])])]) ).

fof(c_0_1584,plain,
    ! [X35,X36,X37] :
      ( ~ linorder(X35)
      | hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less_eq(X35),X36),X37))
      | hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less(X35),X37),X36)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_976])])]) ).

fof(c_0_1585,plain,
    ! [X35,X36,X37] :
      ( ~ linorder(X35)
      | hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less_eq(X35),X36),X37))
      | hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less_eq(X35),X37),X36)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_977])])]) ).

fof(c_0_1586,plain,
    ! [X35,X36,X37] :
      ( ~ linorder(X35)
      | hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less_eq(X35),X36),X37))
      | hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less_eq(X35),X37),X36)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_978])])]) ).

fof(c_0_1587,plain,
    ! [X61,X62] :
      ( ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),esk78_2(X61,X62)),X62))
        | hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X62)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk78_2(X61,X62)),X61))
        | hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X62)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_979])])])]) ).

fof(c_0_1588,plain,
    ! [X4,X5,X6,X7] :
      ( ( hBOOL(hAPP(fun(X4,bool),bool,finite_finite_1(X4),top_top(fun(X4,bool))))
        | ~ hBOOL(hAPP(fun(sum_sum(X4,X5),bool),bool,finite_finite_1(sum_sum(X4,X5)),top_top(fun(sum_sum(X4,X5),bool)))) )
      & ( hBOOL(hAPP(fun(X5,bool),bool,finite_finite_1(X5),top_top(fun(X5,bool))))
        | ~ hBOOL(hAPP(fun(sum_sum(X4,X5),bool),bool,finite_finite_1(sum_sum(X4,X5)),top_top(fun(sum_sum(X4,X5),bool)))) )
      & ( ~ hBOOL(hAPP(fun(X6,bool),bool,finite_finite_1(X6),top_top(fun(X6,bool))))
        | ~ hBOOL(hAPP(fun(X7,bool),bool,finite_finite_1(X7),top_top(fun(X7,bool))))
        | hBOOL(hAPP(fun(sum_sum(X6,X7),bool),bool,finite_finite_1(sum_sum(X6,X7)),top_top(fun(sum_sum(X6,X7),bool)))) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_980])])])])]) ).

fof(c_0_1589,plain,
    ! [X4,X5] :
      ( ~ hBOOL(hAPP(fun(X5,bool),bool,finite_finite_1(X5),top_top(fun(X5,bool))))
      | ~ hBOOL(hAPP(fun(X4,bool),bool,finite_finite_1(X4),top_top(fun(X4,bool))))
      | hBOOL(hAPP(fun(product_prod(X5,X4),bool),bool,finite_finite_1(product_prod(X5,X4)),top_top(fun(product_prod(X5,X4),bool)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_981])]) ).

fof(c_0_1590,plain,
    ! [X35,X36] :
      ( X35 = X36
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X35),X36))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X36),X35)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_982])]) ).

fof(c_0_1591,plain,
    ! [X55,X56,X57,X58] :
      ( ( X55 = X56
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X55),X56))
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X56),X55)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X57),X58))
        | X57 != X58 )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X58),X57))
        | X57 != X58 ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_983])])])])]) ).

fof(c_0_1592,plain,
    ! [X54,X55] :
      ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X55))
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X55),X54)) ),
    inference(variable_rename,[status(thm)],[c_0_984]) ).

fof(c_0_1593,plain,
    ! [X16,X17,X18,X19,X20,X21,X22,X23,X24,X25,X26,X27] :
      ( ( ti(X17,X18) = ti(X17,X20)
        | hAPP(X16,product_prod(X17,X16),hAPP(X17,fun(X16,product_prod(X17,X16)),product_Pair(X17,X16),X18),X19) != hAPP(X16,product_prod(X17,X16),hAPP(X17,fun(X16,product_prod(X17,X16)),product_Pair(X17,X16),X20),X21) )
      & ( ti(X16,X19) = ti(X16,X21)
        | hAPP(X16,product_prod(X17,X16),hAPP(X17,fun(X16,product_prod(X17,X16)),product_Pair(X17,X16),X18),X19) != hAPP(X16,product_prod(X17,X16),hAPP(X17,fun(X16,product_prod(X17,X16)),product_Pair(X17,X16),X20),X21) )
      & ( ti(X23,X24) != ti(X23,X26)
        | ti(X22,X25) != ti(X22,X27)
        | hAPP(X22,product_prod(X23,X22),hAPP(X23,fun(X22,product_prod(X23,X22)),product_Pair(X23,X22),X24),X25) = hAPP(X22,product_prod(X23,X22),hAPP(X23,fun(X22,product_prod(X23,X22)),product_Pair(X23,X22),X26),X27) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_985])])])])]) ).

fof(c_0_1594,plain,
    ! [X25,X26,X27,X28,X29,X30] :
      ( ( ti(X26,X27) = ti(X26,X29)
        | hAPP(X25,product_prod(X26,X25),hAPP(X26,fun(X25,product_prod(X26,X25)),product_Pair(X26,X25),X27),X28) != hAPP(X25,product_prod(X26,X25),hAPP(X26,fun(X25,product_prod(X26,X25)),product_Pair(X26,X25),X29),X30) )
      & ( ti(X25,X28) = ti(X25,X30)
        | hAPP(X25,product_prod(X26,X25),hAPP(X26,fun(X25,product_prod(X26,X25)),product_Pair(X26,X25),X27),X28) != hAPP(X25,product_prod(X26,X25),hAPP(X26,fun(X25,product_prod(X26,X25)),product_Pair(X26,X25),X29),X30) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_986])])]) ).

fof(c_0_1595,plain,
    ! [X40,X41] :
      ( ( hBOOL(hAPP(fun(X40,bool),bool,hAPP(X40,fun(fun(X40,bool),bool),member(X40),esk80_2(X40,X41)),X41))
        | hAPP(fun(X40,bool),nat,finite_card(X40),X41) = zero_zero(nat)
        | ~ hBOOL(hAPP(fun(X40,bool),bool,finite_finite_1(X40),X41)) )
      & ( one_one(nat) != zero_zero(nat)
        | hAPP(fun(X40,bool),nat,finite_card(X40),X41) = zero_zero(nat)
        | ~ hBOOL(hAPP(fun(X40,bool),bool,finite_finite_1(X40),X41)) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_987])])])]) ).

fof(c_0_1596,plain,
    ! [X54,X55] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),hAPP(nat,nat,suc,X55)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),X55)),
    inference(variable_rename,[status(thm)],[c_0_988]) ).

fof(c_0_1597,plain,
    ! [X54,X55] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,X54)),X55) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),hAPP(nat,nat,suc,X55)),
    inference(variable_rename,[status(thm)],[c_0_989]) ).

fof(c_0_1598,plain,
    ! [X4,X5] :
      ( ~ hBOOL(hAPP(fun(fun(X4,X5),bool),bool,finite_finite_1(fun(X4,X5)),top_top(fun(fun(X4,X5),bool))))
      | hAPP(fun(X5,bool),nat,finite_card(X5),top_top(fun(X5,bool))) = hAPP(nat,nat,suc,zero_zero(nat))
      | hBOOL(hAPP(fun(X4,bool),bool,finite_finite_1(X4),top_top(fun(X4,bool)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_990])]) ).

fof(c_0_1599,plain,
    ! [X47,X48,X49] :
      ( ( hAPP(X47,X48,X49,esk35_3(X47,X48,X49)) = hAPP(X47,X48,X49,esk36_3(X47,X48,X49))
        | hBOOL(hAPP(fun(X47,bool),bool,hAPP(fun(X47,X48),fun(fun(X47,bool),bool),inj_on(X47,X48),X49),top_top(fun(X47,bool)))) )
      & ( ti(X47,esk35_3(X47,X48,X49)) != ti(X47,esk36_3(X47,X48,X49))
        | hBOOL(hAPP(fun(X47,bool),bool,hAPP(fun(X47,X48),fun(fun(X47,bool),bool),inj_on(X47,X48),X49),top_top(fun(X47,bool)))) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_991])])])]) ).

fof(c_0_1600,axiom,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),n),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool))))),
    c_0_992 ).

fof(c_0_1601,plain,
    ! [X58,X59] :
      ( ( hBOOL(hAPP(nat,bool,X58,hAPP(nat,nat,suc,esk97_1(X58))))
        | hBOOL(hAPP(nat,bool,X58,zero_zero(nat)))
        | ~ hBOOL(hAPP(nat,bool,X58,X59)) )
      & ( ~ hBOOL(hAPP(nat,bool,X58,esk97_1(X58)))
        | hBOOL(hAPP(nat,bool,X58,zero_zero(nat)))
        | ~ hBOOL(hAPP(nat,bool,X58,X59)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_993])])])])])]) ).

fof(c_0_1602,plain,
    ! [X54] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X54))
      | X54 = hAPP(nat,nat,suc,esk88_1(X54)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_994])])]) ).

fof(c_0_1603,plain,
    ! [X33,X35,X36] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X33))
        | X33 = hAPP(nat,nat,suc,esk84_1(X33)) )
      & ( X35 != hAPP(nat,nat,suc,X36)
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X35)) ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_995])])])])]) ).

fof(c_0_1604,plain,
    ( hBOOL(hAPP(fun(arrow_660593299e_indi,bool),bool,hAPP(fun(arrow_660593299e_indi,nat),fun(fun(arrow_660593299e_indi,bool),bool),inj_on(arrow_660593299e_indi,nat),esk100_0),top_top(fun(arrow_660593299e_indi,bool))))
    & hAPP(fun(arrow_660593299e_indi,bool),fun(nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(fun(arrow_660593299e_indi,bool),fun(nat,bool)),image(arrow_660593299e_indi,nat),esk100_0),top_top(fun(arrow_660593299e_indi,bool))) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool)))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_996])])]) ).

fof(c_0_1605,axiom,
    hAPP(fun(arrow_660593299e_indi,bool),fun(nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(fun(arrow_660593299e_indi,bool),fun(nat,bool)),image(arrow_660593299e_indi,nat),h),top_top(fun(arrow_660593299e_indi,bool))) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool)))),
    c_0_997 ).

fof(c_0_1606,plain,
    ! [X40,X41,X42] : hAPP(fun(X40,fun(X41,bool)),fun(fun(X40,X41),bool),hAPP(fun(X40,bool),fun(fun(X40,fun(X41,bool)),fun(fun(X40,X41),bool)),pi(X40,X41),X42),hAPP(fun(X41,bool),fun(X40,fun(X41,bool)),combk(fun(X41,bool),X40),top_top(fun(X41,bool)))) = top_top(fun(fun(X40,X41),bool)),
    inference(variable_rename,[status(thm)],[c_0_998]) ).

fof(c_0_1607,plain,
    ! [X4] :
      ( ~ linordered_semidom(X4)
      | ~ hBOOL(hAPP(X4,bool,hAPP(X4,fun(X4,bool),ord_less(X4),one_one(X4)),zero_zero(X4))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_999])]) ).

fof(c_0_1608,plain,
    ! [X4] :
      ( ~ linordered_semidom(X4)
      | ~ hBOOL(hAPP(X4,bool,hAPP(X4,fun(X4,bool),ord_less_eq(X4),one_one(X4)),zero_zero(X4))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1000])]) ).

fof(c_0_1609,plain,
    ! [X22,X23] :
      ( ~ top(X22)
      | ~ hBOOL(hAPP(X22,bool,hAPP(X22,fun(X22,bool),ord_less_eq(X22),top_top(X22)),X23))
      | ti(X22,X23) = top_top(X22) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1001])])]) ).

fof(c_0_1610,plain,
    ! [X15,X16,X17] :
      ( ( ~ hBOOL(hAPP(X15,bool,hAPP(X15,fun(X15,bool),ord_less_eq(X15),top_top(X15)),X16))
        | ti(X15,X16) = top_top(X15)
        | ~ top(X15) )
      & ( ti(X15,X17) != top_top(X15)
        | hBOOL(hAPP(X15,bool,hAPP(X15,fun(X15,bool),ord_less_eq(X15),top_top(X15)),X17))
        | ~ top(X15) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1002])])])])]) ).

fof(c_0_1611,plain,
    ! [X18,X19,X20,X21,X22,X23,X24] :
      ( ( hAPP(X18,X18,hAPP(X18,fun(X18,X18),plus_plus(X18),X19),X20) != hAPP(X18,X18,hAPP(X18,fun(X18,X18),plus_plus(X18),X19),X21)
        | ti(X18,X20) = ti(X18,X21)
        | ~ cancel_semigroup_add(X18) )
      & ( ti(X18,X23) != ti(X18,X24)
        | hAPP(X18,X18,hAPP(X18,fun(X18,X18),plus_plus(X18),X22),X23) = hAPP(X18,X18,hAPP(X18,fun(X18,X18),plus_plus(X18),X22),X24)
        | ~ cancel_semigroup_add(X18) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1003])])])])]) ).

fof(c_0_1612,plain,
    ! [X18,X19,X20,X21,X22,X23,X24] :
      ( ( hAPP(X18,X18,hAPP(X18,fun(X18,X18),plus_plus(X18),X19),X20) != hAPP(X18,X18,hAPP(X18,fun(X18,X18),plus_plus(X18),X21),X20)
        | ti(X18,X19) = ti(X18,X21)
        | ~ cancel_semigroup_add(X18) )
      & ( ti(X18,X22) != ti(X18,X24)
        | hAPP(X18,X18,hAPP(X18,fun(X18,X18),plus_plus(X18),X22),X23) = hAPP(X18,X18,hAPP(X18,fun(X18,X18),plus_plus(X18),X24),X23)
        | ~ cancel_semigroup_add(X18) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1004])])])])]) ).

fof(c_0_1613,plain,
    ! [X37,X38,X39,X40] :
      ( ~ cancel_semigroup_add(X37)
      | hAPP(X37,X37,hAPP(X37,fun(X37,X37),plus_plus(X37),X38),X39) != hAPP(X37,X37,hAPP(X37,fun(X37,X37),plus_plus(X37),X38),X40)
      | ti(X37,X39) = ti(X37,X40) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1005])])]) ).

fof(c_0_1614,plain,
    ! [X37,X38,X39,X40] :
      ( ~ cancel146912293up_add(X37)
      | hAPP(X37,X37,hAPP(X37,fun(X37,X37),plus_plus(X37),X38),X39) != hAPP(X37,X37,hAPP(X37,fun(X37,X37),plus_plus(X37),X38),X40)
      | ti(X37,X39) = ti(X37,X40) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1006])])]) ).

fof(c_0_1615,plain,
    ! [X37,X38,X39,X40] :
      ( ~ cancel_semigroup_add(X37)
      | hAPP(X37,X37,hAPP(X37,fun(X37,X37),plus_plus(X37),X38),X39) != hAPP(X37,X37,hAPP(X37,fun(X37,X37),plus_plus(X37),X40),X39)
      | ti(X37,X38) = ti(X37,X40) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1007])])]) ).

fof(c_0_1616,plain,
    ! [X15,X16,X17] :
      ( ( ti(X15,X16) = top_top(X15)
        | hBOOL(hAPP(X15,bool,hAPP(X15,fun(X15,bool),ord_less(X15),X16),top_top(X15)))
        | ~ top(X15) )
      & ( ~ hBOOL(hAPP(X15,bool,hAPP(X15,fun(X15,bool),ord_less(X15),X17),top_top(X15)))
        | ti(X15,X17) != top_top(X15)
        | ~ top(X15) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1008])])])])]) ).

fof(c_0_1617,plain,
    ! [X35,X36,X37] :
      ( ~ order(X35)
      | ~ hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less(X35),X36),X37))
      | ti(X35,X36) != ti(X35,X37) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1009])])]) ).

fof(c_0_1618,plain,
    ! [X35,X36,X37] :
      ( ~ order(X35)
      | ~ hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less(X35),X36),X37))
      | ti(X35,X36) != ti(X35,X37) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1010])])]) ).

fof(c_0_1619,plain,
    ! [X35,X36,X37] :
      ( ~ order(X35)
      | ~ hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less(X35),X36),X37))
      | ti(X35,X37) != ti(X35,X36) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1011])])]) ).

fof(c_0_1620,plain,
    ! [X22,X23] :
      ( ~ top(X22)
      | ~ hBOOL(hAPP(X22,bool,hAPP(X22,fun(X22,bool),ord_less(X22),top_top(X22)),X23)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1012])])]) ).

fof(c_0_1621,plain,
    ! [X54] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,X54))),
    inference(variable_rename,[status(thm)],[c_0_1013]) ).

fof(c_0_1622,plain,
    ! [X35,X36,X37] :
      ( ~ hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),fequal(X35),X36),X37))
      | ti(X35,X36) = ti(X35,X37) ),
    inference(variable_rename,[status(thm)],[c_0_1014]) ).

fof(c_0_1623,plain,
    ! [X54] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),hAPP(nat,nat,suc,X54))),
    inference(variable_rename,[status(thm)],[c_0_1015]) ).

fof(c_0_1624,plain,
    ! [X34,X35] :
      ( ~ preorder(X34)
      | ~ hBOOL(hAPP(X34,bool,hAPP(X34,fun(X34,bool),ord_less(X34),X35),X35)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1016])])]) ).

fof(c_0_1625,plain,
    ! [X30,X31] :
      ( ( X30 = zero_zero(nat)
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X30)) )
      & ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X31))
        | X31 != zero_zero(nat) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1017])])])]) ).

fof(c_0_1626,plain,
    ! [X30,X31] :
      ( ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X30),zero_zero(nat)))
        | X30 = zero_zero(nat) )
      & ( X31 != zero_zero(nat)
        | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X31),zero_zero(nat))) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1018])])])]) ).

fof(c_0_1627,plain,
    ! [X54] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),zero_zero(nat))),
    inference(variable_rename,[status(thm)],[c_0_1019]) ).

fof(c_0_1628,plain,
    ! [X54] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),zero_zero(nat))),
    inference(variable_rename,[status(thm)],[c_0_1020]) ).

fof(c_0_1629,plain,
    ! [X54] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),zero_zero(nat))),
    inference(variable_rename,[status(thm)],[c_0_1021]) ).

fof(c_0_1630,plain,
    ! [X54,X55] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X55))
      | X55 != zero_zero(nat) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1022])]) ).

fof(c_0_1631,plain,
    ! [X57,X58] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X57),X58))
      | X57 != X58 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1023])]) ).

fof(c_0_1632,plain,
    ! [X54,X55] :
      ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X55))
      | X55 != X54 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1024])]) ).

fof(c_0_1633,plain,
    ! [X54] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X54)),
    inference(variable_rename,[status(thm)],[c_0_1025]) ).

fof(c_0_1634,plain,
    ! [X54] : ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X54),X54)),
    inference(variable_rename,[status(thm)],[c_0_1026]) ).

fof(c_0_1635,plain,
    ! [X58,X59,X60,X61,X62,X63] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X58),X59) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X60),X59)
        | X58 = X60 )
      & ( X61 != X63
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X61),X62) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X63),X62) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1027])])])]) ).

fof(c_0_1636,plain,
    ! [X58,X59,X60,X61,X62,X63] :
      ( ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X58),X59) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X58),X60)
        | X59 = X60 )
      & ( X62 != X63
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X61),X62) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X61),X63) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1028])])])]) ).

fof(c_0_1637,plain,
    ! [X88,X89] :
      ( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X88),X89))
      | hBOOL(X88)
      | hBOOL(X89) ),
    inference(variable_rename,[status(thm)],[c_0_1029]) ).

fof(c_0_1638,plain,
    ! [X88,X89] :
      ( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X88),X89))
      | hBOOL(X89) ),
    inference(variable_rename,[status(thm)],[c_0_1030]) ).

fof(c_0_1639,plain,
    ! [X88,X89] :
      ( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X88),X89))
      | hBOOL(X88) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[c_0_1031])])]) ).

fof(c_0_1640,plain,
    ! [X39,X40,X41,X42] :
      ( hAPP(X39,X40,X41,esk20_4(X39,X40,X41,X42)) != hAPP(X39,X40,X42,esk20_4(X39,X40,X41,X42))
      | ti(fun(X39,X40),X41) = ti(fun(X39,X40),X42) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1032])])]) ).

fof(c_0_1641,plain,
    ! [X4,X5] :
      ( ~ hBOOL(hAPP(fun(fun(X4,X5),bool),bool,finite_finite_1(fun(X4,X5)),top_top(fun(fun(X4,X5),bool))))
      | hBOOL(hAPP(fun(X5,bool),bool,finite_finite_1(X5),top_top(fun(X5,bool)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1033])]) ).

fof(c_0_1642,plain,
    ! [X44,X45,X46] :
      ( ti(fun(X44,bool),X45) != ti(fun(X44,bool),X46)
      | hBOOL(hAPP(fun(X44,bool),bool,hAPP(fun(X44,bool),fun(fun(X44,bool),bool),ord_less_eq(fun(X44,bool)),X45),X46)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1034])]) ).

fof(c_0_1643,plain,
    ! [X44,X45,X46] :
      ( ti(fun(X44,bool),X45) != ti(fun(X44,bool),X46)
      | hBOOL(hAPP(fun(X44,bool),bool,hAPP(fun(X44,bool),fun(fun(X44,bool),bool),ord_less_eq(fun(X44,bool)),X46),X45)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1035])]) ).

fof(c_0_1644,plain,
    ! [X44,X45,X46] :
      ( ( hBOOL(hAPP(fun(X44,bool),bool,hAPP(fun(X44,bool),fun(fun(X44,bool),bool),ord_less_eq(fun(X44,bool)),X45),X46))
        | ti(fun(X44,bool),X45) != ti(fun(X44,bool),X46) )
      & ( hBOOL(hAPP(fun(X44,bool),bool,hAPP(fun(X44,bool),fun(fun(X44,bool),bool),ord_less_eq(fun(X44,bool)),X46),X45))
        | ti(fun(X44,bool),X45) != ti(fun(X44,bool),X46) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1036])])]) ).

fof(c_0_1645,plain,
    ! [X40,X41] : hBOOL(hAPP(fun(X40,bool),bool,hAPP(fun(X40,bool),fun(fun(X40,bool),bool),ord_less_eq(fun(X40,bool)),X41),top_top(fun(X40,bool)))),
    inference(variable_rename,[status(thm)],[c_0_1037]) ).

fof(c_0_1646,plain,
    ! [X35,X36,X37] : hAPP(X35,X35,hAPP(X35,fun(X35,X35),hAPP(bool,fun(X35,fun(X35,X35)),if(X35),fFalse),X36),X37) = ti(X35,X37),
    inference(variable_rename,[status(thm)],[c_0_1038]) ).

fof(c_0_1647,plain,
    ! [X35,X36,X37] : hAPP(X35,X35,hAPP(X35,fun(X35,X35),hAPP(bool,fun(X35,fun(X35,X35)),if(X35),fTrue),X36),X37) = ti(X35,X36),
    inference(variable_rename,[status(thm)],[c_0_1039]) ).

fof(c_0_1648,plain,
    ! [X55,X56,X57,X58] :
      ( ( X55 = zero_zero(nat)
        | X55 = hAPP(nat,nat,suc,zero_zero(nat))
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X55),X56) != hAPP(nat,nat,suc,zero_zero(nat)) )
      & ( X56 = hAPP(nat,nat,suc,zero_zero(nat))
        | X55 = hAPP(nat,nat,suc,zero_zero(nat))
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X55),X56) != hAPP(nat,nat,suc,zero_zero(nat)) )
      & ( X55 = zero_zero(nat)
        | X56 = zero_zero(nat)
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X55),X56) != hAPP(nat,nat,suc,zero_zero(nat)) )
      & ( X56 = hAPP(nat,nat,suc,zero_zero(nat))
        | X56 = zero_zero(nat)
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X55),X56) != hAPP(nat,nat,suc,zero_zero(nat)) )
      & ( X57 != hAPP(nat,nat,suc,zero_zero(nat))
        | X58 != zero_zero(nat)
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X57),X58) = hAPP(nat,nat,suc,zero_zero(nat)) )
      & ( X57 != zero_zero(nat)
        | X58 != hAPP(nat,nat,suc,zero_zero(nat))
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X57),X58) = hAPP(nat,nat,suc,zero_zero(nat)) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1040])])])])]) ).

fof(c_0_1649,plain,
    ! [X55,X56,X57,X58] :
      ( ( X55 = zero_zero(nat)
        | X55 = hAPP(nat,nat,suc,zero_zero(nat))
        | hAPP(nat,nat,suc,zero_zero(nat)) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X55),X56) )
      & ( X56 = hAPP(nat,nat,suc,zero_zero(nat))
        | X55 = hAPP(nat,nat,suc,zero_zero(nat))
        | hAPP(nat,nat,suc,zero_zero(nat)) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X55),X56) )
      & ( X55 = zero_zero(nat)
        | X56 = zero_zero(nat)
        | hAPP(nat,nat,suc,zero_zero(nat)) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X55),X56) )
      & ( X56 = hAPP(nat,nat,suc,zero_zero(nat))
        | X56 = zero_zero(nat)
        | hAPP(nat,nat,suc,zero_zero(nat)) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X55),X56) )
      & ( X57 != hAPP(nat,nat,suc,zero_zero(nat))
        | X58 != zero_zero(nat)
        | hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X57),X58) )
      & ( X57 != zero_zero(nat)
        | X58 != hAPP(nat,nat,suc,zero_zero(nat))
        | hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X57),X58) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1041])])])])]) ).

fof(c_0_1650,plain,
    ! [X40,X41] : hBOOL(hAPP(fun(X40,bool),bool,hAPP(fun(X40,bool),fun(fun(X40,bool),bool),ord_less_eq(fun(X40,bool)),X41),X41)),
    inference(variable_rename,[status(thm)],[c_0_1042]) ).

fof(c_0_1651,plain,
    ! [X40,X41] :
      ( ~ hBOOL(hAPP(fun(X40,bool),bool,finite_finite_1(X40),top_top(fun(X40,bool))))
      | hAPP(fun(X40,bool),nat,finite_card(X40),X41) != hAPP(fun(X40,bool),nat,finite_card(X40),top_top(fun(X40,bool)))
      | ti(fun(X40,bool),X41) = top_top(fun(X40,bool)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1043])])])]) ).

fof(c_0_1652,plain,
    ! [X40,X41] : hBOOL(hAPP(fun(X40,bool),bool,hAPP(fun(X40,X40),fun(fun(X40,bool),bool),inj_on(X40,X40),combi(X40)),X41)),
    inference(variable_rename,[status(thm)],[c_0_1044]) ).

fof(c_0_1653,axiom,
    hBOOL(hAPP(fun(arrow_660593299e_indi,bool),bool,hAPP(fun(arrow_660593299e_indi,nat),fun(fun(arrow_660593299e_indi,bool),bool),inj_on(arrow_660593299e_indi,nat),h),top_top(fun(arrow_660593299e_indi,bool)))),
    c_0_1045 ).

fof(c_0_1654,plain,
    ! [X4,X5] : ti(fun(fun(X4,fun(X4,X4)),fun(X4,fun(fun(X5,X4),fun(fun(fun(X5,bool),X4),bool)))),finite908156982e_idem(X4,X5)) = finite908156982e_idem(X4,X5),
    inference(variable_rename,[status(thm)],[c_0_1046]) ).

fof(c_0_1655,plain,
    ! [X7,X8] : hBOOL(hAPP(fun(X7,bool),bool,hAPP(X7,fun(fun(X7,bool),bool),member(X7),X8),top_top(fun(X7,bool)))),
    inference(variable_rename,[status(thm)],[c_0_1047]) ).

fof(c_0_1656,plain,
    ! [X7,X8] : hBOOL(hAPP(fun(X7,bool),bool,hAPP(X7,fun(fun(X7,bool),bool),member(X7),X8),top_top(fun(X7,bool)))),
    inference(variable_rename,[status(thm)],[c_0_1048]) ).

fof(c_0_1657,plain,
    ! [X61] : hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,nat),fun(fun(nat,bool),bool),inj_on(nat,nat),suc),X61)),
    inference(variable_rename,[status(thm)],[c_0_1049]) ).

fof(c_0_1658,plain,
    ! [X4] :
      ( ~ ring_1(X4)
      | hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),one_one(X4)),ring_1_Ints(X4))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1050])]) ).

fof(c_0_1659,plain,
    ! [X4] :
      ( ~ ring_1(X4)
      | hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),zero_zero(X4)),ring_1_Ints(X4))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1051])]) ).

fof(c_0_1660,plain,
    ! [X4,X5] :
      ( ( ~ hBOOL(hAPP(fun(option(X4),bool),bool,finite_finite_1(option(X4)),top_top(fun(option(X4),bool))))
        | hBOOL(hAPP(fun(X4,bool),bool,finite_finite_1(X4),top_top(fun(X4,bool)))) )
      & ( ~ hBOOL(hAPP(fun(X5,bool),bool,finite_finite_1(X5),top_top(fun(X5,bool))))
        | hBOOL(hAPP(fun(option(X5),bool),bool,finite_finite_1(option(X5)),top_top(fun(option(X5),bool)))) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1052])])])]) ).

fof(c_0_1661,plain,
    ! [X35,X36,X37] :
      ( ti(X35,X36) != ti(X35,X37)
      | hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),fequal(X35),X36),X37)) ),
    inference(variable_rename,[status(thm)],[c_0_1053]) ).

fof(c_0_1662,plain,
    ! [X4] :
      ( ~ linordered_semidom(X4)
      | hBOOL(hAPP(X4,bool,hAPP(X4,fun(X4,bool),ord_less(X4),zero_zero(X4)),one_one(X4))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1054])]) ).

fof(c_0_1663,plain,
    ! [X4] :
      ( ~ linordered_semidom(X4)
      | hBOOL(hAPP(X4,bool,hAPP(X4,fun(X4,bool),ord_less_eq(X4),zero_zero(X4)),one_one(X4))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1055])]) ).

fof(c_0_1664,plain,
    ! [X37,X38,X39] :
      ( ~ comm_semiring_1(X37)
      | hAPP(X37,X37,hAPP(X37,fun(X37,X37),plus_plus(X37),X38),X39) = hAPP(X37,X37,hAPP(X37,fun(X37,X37),plus_plus(X37),X39),X38) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1056])])]) ).

fof(c_0_1665,plain,
    ! [X22,X23] :
      ( ~ top(X22)
      | hBOOL(hAPP(X22,bool,hAPP(X22,fun(X22,bool),ord_less_eq(X22),X23),top_top(X22))) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1057])])]) ).

fof(c_0_1666,plain,
    ! [X4,X5] : hAPP(fun(X4,bool),fun(sum_sum(X5,X4),bool),hAPP(fun(X5,bool),fun(fun(X4,bool),fun(sum_sum(X5,X4),bool)),sum_Plus(X5,X4),top_top(fun(X5,bool))),top_top(fun(X4,bool))) = top_top(fun(sum_sum(X5,X4),bool)),
    inference(variable_rename,[status(thm)],[c_0_1058]) ).

fof(c_0_1667,plain,
    ! [X35,X36,X37] :
      ( ~ preorder(X35)
      | X36 != X37
      | hBOOL(hAPP(X35,bool,hAPP(X35,fun(X35,bool),ord_less_eq(X35),X36),X37)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1059])])]) ).

fof(c_0_1668,plain,
    ! [X34,X35] :
      ( ~ preorder(X34)
      | hBOOL(hAPP(X34,bool,hAPP(X34,fun(X34,bool),ord_less_eq(X34),X35),X35)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1060])])]) ).

fof(c_0_1669,plain,
    ! [X54] :
      ( X54 = zero_zero(nat)
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X54)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1061])]) ).

fof(c_0_1670,plain,
    ! [X54] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),X54)),
    inference(variable_rename,[status(thm)],[c_0_1062]) ).

fof(c_0_1671,plain,
    ! [X54] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),X54)),
    inference(variable_rename,[status(thm)],[c_0_1063]) ).

fof(c_0_1672,plain,
    ! [X54,X55] :
      ( X54 != X55
      | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X55)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1064])]) ).

fof(c_0_1673,plain,
    ! [X54] : hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X54),X54)),
    inference(variable_rename,[status(thm)],[c_0_1065]) ).

fof(c_0_1674,plain,
    ! [X54,X55] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),X55) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X55),X54),
    inference(variable_rename,[status(thm)],[c_0_1066]) ).

fof(c_0_1675,plain,
    ! [X88,X89] :
      ( ~ hBOOL(X89)
      | ~ hBOOL(X88)
      | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X89),X88)) ),
    inference(variable_rename,[status(thm)],[c_0_1067]) ).

fof(c_0_1676,plain,
    ! [X88,X89] :
      ( ~ hBOOL(X89)
      | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X88),X89)) ),
    inference(variable_rename,[status(thm)],[c_0_1068]) ).

fof(c_0_1677,plain,
    ! [X88,X89] :
      ( ~ hBOOL(X89)
      | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X89),X88)) ),
    inference(variable_rename,[status(thm)],[c_0_1069]) ).

fof(c_0_1678,axiom,
    hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,f)),
    c_0_1070 ).

fof(c_0_1679,axiom,
    hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,f)),
    c_0_1071 ).

fof(c_0_1680,plain,
    ! [X16,X17,X18,X19,X20] :
      ( ( ti(X16,X17) != hAPP(X16,X16,hAPP(X16,fun(X16,X16),plus_plus(X16),X17),X18)
        | ti(X16,X18) = zero_zero(X16)
        | ~ semiri456707255roduct(X16) )
      & ( ti(X16,X20) != zero_zero(X16)
        | ti(X16,X19) = hAPP(X16,X16,hAPP(X16,fun(X16,X16),plus_plus(X16),X19),X20)
        | ~ semiri456707255roduct(X16) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1072])])])])]) ).

fof(c_0_1681,plain,
    ! [X15,X16,X17] :
      ( ( hAPP(X15,X15,hAPP(X15,fun(X15,X15),plus_plus(X15),X16),X16) != zero_zero(X15)
        | ti(X15,X16) = zero_zero(X15)
        | ~ linord219039673up_add(X15) )
      & ( ti(X15,X17) != zero_zero(X15)
        | hAPP(X15,X15,hAPP(X15,fun(X15,X15),plus_plus(X15),X17),X17) = zero_zero(X15)
        | ~ linord219039673up_add(X15) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1073])])])])]) ).

fof(c_0_1682,plain,
    ! [X15,X16,X17] :
      ( ( zero_zero(X15) != hAPP(X15,X15,hAPP(X15,fun(X15,X15),plus_plus(X15),X16),X16)
        | ti(X15,X16) = zero_zero(X15)
        | ~ linord219039673up_add(X15) )
      & ( ti(X15,X17) != zero_zero(X15)
        | zero_zero(X15) = hAPP(X15,X15,hAPP(X15,fun(X15,X15),plus_plus(X15),X17),X17)
        | ~ linord219039673up_add(X15) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1074])])])])]) ).

fof(c_0_1683,plain,
    ! [X55,X56,X57,X58] :
      ( ( X55 = zero_zero(nat)
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X55),X56) != zero_zero(nat) )
      & ( X56 = zero_zero(nat)
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X55),X56) != zero_zero(nat) )
      & ( X57 != zero_zero(nat)
        | X58 != zero_zero(nat)
        | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X57),X58) = zero_zero(nat) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1075])])])])]) ).

fof(c_0_1684,plain,
    ! [X54,X55] :
      ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),X55) != X54
      | X55 = zero_zero(nat) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1076])]) ).

fof(c_0_1685,plain,
    ! [X81,X82] : hAPP(fun(X81,bool),fun(X81,bool),hAPP(fun(X81,X81),fun(fun(X81,bool),fun(X81,bool)),image(X81,X81),combi(X81)),X82) = ti(fun(X81,bool),X82),
    inference(variable_rename,[status(thm)],[c_0_1077]) ).

fof(c_0_1686,plain,
    ! [X54] : hAPP(nat,nat,suc,X54) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),X54),
    inference(variable_rename,[status(thm)],[c_0_1078]) ).

fof(c_0_1687,plain,
    ! [X54] : hAPP(nat,nat,suc,X54) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X54),one_one(nat)),
    inference(variable_rename,[status(thm)],[c_0_1079]) ).

fof(c_0_1688,plain,
    ! [X27] : hAPP(nat,fun(nat,bool),ord_less(nat),X27) = hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X27)),
    inference(variable_rename,[status(thm)],[c_0_1080]) ).

fof(c_0_1689,plain,
    ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),top_top(fun(nat,bool)))),
    c_0_1081 ).

fof(c_0_1690,plain,
    ! [X4] : ti(fun(fun(nat,fun(nat,nat)),fun(fun(X4,nat),fun(nat,fun(fun(X4,bool),nat)))),finite_fold_image(nat,X4)) = finite_fold_image(nat,X4),
    inference(variable_rename,[status(thm)],[c_0_1082]) ).

fof(c_0_1691,axiom,
    ti(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool)),arrow_218898985ctator) = arrow_218898985ctator,
    c_0_1083 ).

fof(c_0_1692,axiom,
    ti(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),arrow_831799591nimity) = arrow_831799591nimity,
    c_0_1084 ).

fof(c_0_1693,axiom,
    ti(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),arrow_2037941124le_IIA) = arrow_2037941124le_IIA,
    c_0_1085 ).

fof(c_0_1694,plain,
    ! [X4] : top_top(fun(X4,bool)) = hAPP(fun(X4,bool),fun(X4,bool),collect(X4),hAPP(bool,fun(X4,bool),combk(bool,X4),fTrue)),
    inference(variable_rename,[status(thm)],[c_0_1086]) ).

fof(c_0_1695,plain,
    ! [X88,X89,X90,X91] : hAPP(X88,X89,hAPP(X89,fun(X88,X89),combk(X89,X88),X90),X91) = ti(X89,X90),
    inference(variable_rename,[status(thm)],[c_0_1087]) ).

fof(c_0_1696,plain,
    ! [X22,X23] :
      ( ~ comm_semiring_1(X22)
      | hAPP(X22,X22,hAPP(X22,fun(X22,X22),plus_plus(X22),zero_zero(X22)),X23) = ti(X22,X23) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1088])])]) ).

fof(c_0_1697,plain,
    ! [X22,X23] :
      ( ~ monoid_add(X22)
      | hAPP(X22,X22,hAPP(X22,fun(X22,X22),plus_plus(X22),zero_zero(X22)),X23) = ti(X22,X23) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1089])])]) ).

fof(c_0_1698,plain,
    ! [X22,X23] :
      ( ~ comm_monoid_add(X22)
      | hAPP(X22,X22,hAPP(X22,fun(X22,X22),plus_plus(X22),zero_zero(X22)),X23) = ti(X22,X23) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1090])])]) ).

fof(c_0_1699,plain,
    ! [X22,X23] :
      ( ~ comm_semiring_1(X22)
      | hAPP(X22,X22,hAPP(X22,fun(X22,X22),plus_plus(X22),X23),zero_zero(X22)) = ti(X22,X23) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1091])])]) ).

fof(c_0_1700,plain,
    ! [X22,X23] :
      ( ~ monoid_add(X22)
      | hAPP(X22,X22,hAPP(X22,fun(X22,X22),plus_plus(X22),X23),zero_zero(X22)) = ti(X22,X23) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1092])])]) ).

fof(c_0_1701,plain,
    ! [X22,X23] :
      ( ~ comm_monoid_add(X22)
      | hAPP(X22,X22,hAPP(X22,fun(X22,X22),plus_plus(X22),X23),zero_zero(X22)) = ti(X22,X23) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1093])])]) ).

fof(c_0_1702,plain,
    ! [X40,X41] :
      ( hBOOL(hAPP(fun(X40,bool),bool,finite_finite_1(X40),X41))
      | hAPP(fun(X40,bool),nat,finite_card(X40),X41) = zero_zero(nat) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1094])]) ).

fof(c_0_1703,axiom,
    ti(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),arrow_1322701812_below) = arrow_1322701812_below,
    c_0_1095 ).

fof(c_0_1704,axiom,
    ti(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),arrow_14103264_above) = arrow_14103264_above,
    c_0_1096 ).

fof(c_0_1705,plain,
    ! [X54] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),X54) = X54,
    inference(variable_rename,[status(thm)],[c_0_1097]) ).

fof(c_0_1706,plain,
    ! [X52] : hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X52),zero_zero(nat)) = X52,
    inference(variable_rename,[status(thm)],[c_0_1098]) ).

fof(c_0_1707,plain,
    ! [X87] :
      ( ~ hBOOL(hAPP(bool,bool,fNot,X87))
      | ~ hBOOL(X87) ),
    inference(variable_rename,[status(thm)],[c_0_1099]) ).

fof(c_0_1708,plain,
    ! [X69,X70,X71,X72] :
      ( ( hAPP(nat,nat,suc,X69) != hAPP(nat,nat,suc,X70)
        | X69 = X70 )
      & ( X71 != X72
        | hAPP(nat,nat,suc,X71) = hAPP(nat,nat,suc,X72) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1100])])])]) ).

fof(c_0_1709,plain,
    ! [X35,X36] :
      ( hAPP(nat,nat,suc,X35) != hAPP(nat,nat,suc,X36)
      | X35 = X36 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1101])]) ).

fof(c_0_1710,plain,
    ! [X4,X5] : ti(fun(fun(X4,bool),fun(fun(X4,fun(X5,bool)),fun(fun(X4,X5),bool))),pi(X4,X5)) = pi(X4,X5),
    inference(variable_rename,[status(thm)],[c_0_1102]) ).

fof(c_0_1711,plain,
    ! [X6,X7,X8,X9] : ti(X6,hAPP(X7,X6,X8,X9)) = hAPP(X7,X6,X8,X9),
    inference(variable_rename,[status(thm)],[c_0_1103]) ).

fof(c_0_1712,plain,
    ! [X4] :
      ( ~ finite_finite(X4)
      | hBOOL(hAPP(fun(X4,bool),bool,finite_finite_1(X4),top_top(fun(X4,bool)))) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1104])]) ).

fof(c_0_1713,axiom,
    hBOOL(hAPP(fun(arrow_660593299e_indi,bool),bool,finite_finite_1(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool)))),
    c_0_1105 ).

fof(c_0_1714,plain,
    ! [X4,X5,X6] : ti(fun(fun(X4,fun(X5,X6)),fun(fun(X4,X5),fun(X4,X6))),combs(X4,X5,X6)) = combs(X4,X5,X6),
    inference(variable_rename,[status(thm)],[c_0_1106]) ).

fof(c_0_1715,plain,
    ! [X7,X8] : hBOOL(hAPP(X7,bool,top_top(fun(X7,bool)),X8)),
    inference(variable_rename,[status(thm)],[c_0_1107]) ).

fof(c_0_1716,plain,
    ! [X6,X7,X8,X9] : hAPP(X6,X7,ti(fun(X6,X7),X8),X9) = hAPP(X6,X7,X8,X9),
    inference(variable_rename,[status(thm)],[c_0_1108]) ).

fof(c_0_1717,plain,
    ! [X4,X5] : ti(fun(fun(X4,bool),fun(fun(X5,bool),fun(sum_sum(X4,X5),bool))),sum_Plus(X4,X5)) = sum_Plus(X4,X5),
    inference(variable_rename,[status(thm)],[c_0_1109]) ).

fof(c_0_1718,plain,
    ! [X40,X41] :
      ( ~ finite_finite(X40)
      | hBOOL(hAPP(fun(X40,bool),bool,finite_finite_1(X40),X41)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1110])])]) ).

fof(c_0_1719,plain,
    ! [X40,X41] :
      ( ~ finite_finite(X40)
      | hBOOL(hAPP(fun(X40,bool),bool,finite_finite_1(X40),X41)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1111])])]) ).

fof(c_0_1720,plain,
    ! [X6,X7,X8,X9] : hAPP(X6,X7,X8,ti(X6,X9)) = hAPP(X6,X7,X8,X9),
    inference(variable_rename,[status(thm)],[c_0_1112]) ).

fof(c_0_1721,plain,
    ! [X4,X5,X6] : ti(fun(fun(X4,fun(X5,X6)),fun(product_prod(X4,X5),X6)),product_prod_rec(X4,X5,X6)) = product_prod_rec(X4,X5,X6),
    inference(variable_rename,[status(thm)],[c_0_1113]) ).

fof(c_0_1722,plain,
    ! [X4,X5,X6] : ti(fun(fun(X4,fun(X5,X6)),fun(X5,fun(X4,X6))),combc(X4,X5,X6)) = combc(X4,X5,X6),
    inference(variable_rename,[status(thm)],[c_0_1114]) ).

fof(c_0_1723,plain,
    ! [X4,X5,X6] : ti(fun(fun(X4,X5),fun(fun(X6,X4),fun(X6,X5))),combb(X4,X5,X6)) = combb(X4,X5,X6),
    inference(variable_rename,[status(thm)],[c_0_1115]) ).

fof(c_0_1724,plain,
    ! [X87] :
      ( hBOOL(X87)
      | hBOOL(hAPP(bool,bool,fNot,X87)) ),
    inference(variable_rename,[status(thm)],[c_0_1116]) ).

fof(c_0_1725,axiom,
    ti(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1427655034_mktop) = arrow_1427655034_mktop,
    c_0_1117 ).

fof(c_0_1726,axiom,
    ti(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1278947948_mkbot) = arrow_1278947948_mkbot,
    c_0_1118 ).

fof(c_0_1727,plain,
    ! [X52] : zero_zero(nat) != hAPP(nat,nat,suc,X52),
    inference(variable_rename,[status(thm)],[c_0_1119]) ).

fof(c_0_1728,plain,
    ! [X71] : zero_zero(nat) != hAPP(nat,nat,suc,X71),
    inference(variable_rename,[status(thm)],[c_0_1120]) ).

fof(c_0_1729,plain,
    ! [X52] : hAPP(nat,nat,suc,X52) != zero_zero(nat),
    inference(variable_rename,[status(thm)],[c_0_1121]) ).

fof(c_0_1730,plain,
    ! [X70] : hAPP(nat,nat,suc,X70) != zero_zero(nat),
    inference(variable_rename,[status(thm)],[c_0_1122]) ).

fof(c_0_1731,plain,
    ! [X52] : zero_zero(nat) != hAPP(nat,nat,suc,X52),
    inference(variable_rename,[status(thm)],[c_0_1123]) ).

fof(c_0_1732,plain,
    ! [X52] : hAPP(nat,nat,suc,X52) != zero_zero(nat),
    inference(variable_rename,[status(thm)],[c_0_1124]) ).

fof(c_0_1733,plain,
    ! [X4,X5] : ti(fun(fun(X4,bool),fun(fun(X4,X5),fun(X5,X4))),hilbert_inv_into(X4,X5)) = hilbert_inv_into(X4,X5),
    inference(variable_rename,[status(thm)],[c_0_1125]) ).

fof(c_0_1734,plain,
    ! [X54] : X54 != hAPP(nat,nat,suc,X54),
    inference(variable_rename,[status(thm)],[c_0_1126]) ).

fof(c_0_1735,plain,
    ! [X54] : hAPP(nat,nat,suc,X54) != X54,
    inference(variable_rename,[status(thm)],[c_0_1127]) ).

fof(c_0_1736,plain,
    ! [X4,X5] : ti(fun(fun(product_prod(X4,X5),bool),fun(X4,fun(X5,bool))),in_rel(X4,X5)) = in_rel(X4,X5),
    inference(variable_rename,[status(thm)],[c_0_1128]) ).

fof(c_0_1737,plain,
    ! [X4,X5] : ti(fun(fun(X4,X5),fun(fun(X4,bool),fun(X5,bool))),image(X4,X5)) = image(X4,X5),
    inference(variable_rename,[status(thm)],[c_0_1129]) ).

fof(c_0_1738,plain,
    ! [X12,X13] : hAPP(fun(X12,bool),fun(X12,bool),collect(X12),X13) = ti(fun(X12,bool),X13),
    inference(variable_rename,[status(thm)],[c_0_1130]) ).

fof(c_0_1739,axiom,
    ti(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),arrow_1111136790e_Prof) = arrow_1111136790e_Prof,
    c_0_1131 ).

fof(c_0_1740,axiom,
    hAPP(fun(product_unit,bool),nat,finite_card(product_unit),top_top(fun(product_unit,bool))) = one_one(nat),
    c_0_1132 ).

fof(c_0_1741,plain,
    ! [X7,X8,X9] :
      ( ~ top(X8)
      | hAPP(X7,X8,top_top(fun(X7,X8)),X9) = top_top(X8) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1133])])]) ).

fof(c_0_1742,plain,
    ! [X4,X5] : ti(fun(fun(X4,X5),fun(fun(X4,bool),bool)),inj_on(X4,X5)) = inj_on(X4,X5),
    inference(variable_rename,[status(thm)],[c_0_1134]) ).

fof(c_0_1743,plain,
    ! [X87,X88] : hAPP(X87,X87,combi(X87),X88) = ti(X87,X88),
    inference(variable_rename,[status(thm)],[c_0_1135]) ).

fof(c_0_1744,plain,
    ! [X75] :
      ( X75 = zero_zero(nat)
      | X75 = hAPP(nat,nat,suc,esk96_1(X75)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1136])])]) ).

fof(c_0_1745,plain,
    ! [X54] :
      ( X54 = zero_zero(nat)
      | X54 = hAPP(nat,nat,suc,esk95_1(X54)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1137])])]) ).

fof(c_0_1746,axiom,
    one_one(nat) = hAPP(nat,nat,suc,zero_zero(nat)),
    c_0_1138 ).

fof(c_0_1747,plain,
    ! [X4,X5] : ti(fun(X4,fun(X5,product_prod(X4,X5))),product_Pair(X4,X5)) = product_Pair(X4,X5),
    inference(variable_rename,[status(thm)],[c_0_1139]) ).

fof(c_0_1748,plain,
    ! [X4] : ti(fun(bool,fun(X4,fun(X4,X4))),if(X4)) = if(X4),
    inference(variable_rename,[status(thm)],[c_0_1140]) ).

fof(c_0_1749,plain,
    ! [X4] :
      ( ~ linorder(X4)
      | ti(fun(X4,fun(X4,fun(X4,bool))),ord_atLeastLessThan(X4)) = ord_atLeastLessThan(X4) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1141])]) ).

fof(c_0_1750,plain,
    ! [X4] : ti(fun(X4,fun(fun(X4,bool),bool)),member(X4)) = member(X4),
    inference(variable_rename,[status(thm)],[c_0_1142]) ).

fof(c_0_1751,axiom,
    ti(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),arrow_2064824852le_Lin) = arrow_2064824852le_Lin,
    c_0_1143 ).

fof(c_0_1752,plain,
    ! [X4] : ti(fun(fun(X4,bool),fun(X4,bool)),collect(X4)) = collect(X4),
    inference(variable_rename,[status(thm)],[c_0_1144]) ).

fof(c_0_1753,plain,
    ! [X4,X5] : ti(fun(X4,fun(X5,X4)),combk(X4,X5)) = combk(X4,X5),
    inference(variable_rename,[status(thm)],[c_0_1145]) ).

fof(c_0_1754,plain,
    ! [X4] :
      ( ~ cancel_semigroup_add(X4)
      | ti(fun(X4,fun(X4,X4)),plus_plus(X4)) = plus_plus(X4) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1146])]) ).

fof(c_0_1755,plain,
    ! [X4] :
      ( ~ ab_semigroup_add(X4)
      | ti(fun(X4,fun(X4,X4)),plus_plus(X4)) = plus_plus(X4) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1147])]) ).

fof(c_0_1756,plain,
    ! [X4] :
      ( ~ monoid_add(X4)
      | ti(fun(X4,fun(X4,X4)),plus_plus(X4)) = plus_plus(X4) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1148])]) ).

fof(c_0_1757,plain,
    ! [X2] :
      ( ~ ord(X2)
      | ti(fun(X2,fun(X2,bool)),ord_less_eq(X2)) = ord_less_eq(X2) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1149])]) ).

fof(c_0_1758,plain,
    ! [X4] :
      ( ~ ord(X4)
      | ti(fun(X4,fun(X4,bool)),ord_less(X4)) = ord_less(X4) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1150])]) ).

fof(c_0_1759,plain,
    ! [X4] : ti(fun(X4,fun(X4,bool)),fequal(X4)) = fequal(X4),
    inference(variable_rename,[status(thm)],[c_0_1151]) ).

fof(c_0_1760,plain,
    ! [X2] : ti(fun(fun(X2,bool),bool),finite_finite_1(X2)) = finite_finite_1(X2),
    inference(variable_rename,[status(thm)],[c_0_1152]) ).

fof(c_0_1761,plain,
    ! [X4] : ti(fun(fun(X4,bool),nat),finite_card(X4)) = finite_card(X4),
    inference(variable_rename,[status(thm)],[c_0_1153]) ).

fof(c_0_1762,axiom,
    ti(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),lba) = lba,
    c_0_1154 ).

fof(c_0_1763,axiom,
    ti(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),lab) = lab,
    c_0_1155 ).

fof(c_0_1764,axiom,
    ti(fun(bool,fun(bool,bool)),fdisj) = fdisj,
    c_0_1156 ).

fof(c_0_1765,axiom,
    ti(fun(bool,fun(bool,bool)),fconj) = fconj,
    c_0_1157 ).

fof(c_0_1766,plain,
    ! [X4] :
      ( ~ ring_1(X4)
      | ti(fun(X4,bool),ring_1_Ints(X4)) = ring_1_Ints(X4) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1158])]) ).

fof(c_0_1767,plain,
    ! [X7,X8,X9] :
      ( ( zero_zero(X7) != ti(X7,X8)
        | ti(X7,X8) = zero_zero(X7)
        | ~ zero(X7) )
      & ( ti(X7,X9) != zero_zero(X7)
        | zero_zero(X7) = ti(X7,X9)
        | ~ zero(X7) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1159])])])])]) ).

fof(c_0_1768,plain,
    ! [X7,X8,X9] :
      ( ( one_one(X7) != ti(X7,X8)
        | ti(X7,X8) = one_one(X7)
        | ~ one(X7) )
      & ( ti(X7,X9) != one_one(X7)
        | one_one(X7) = ti(X7,X9)
        | ~ one(X7) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1160])])])])]) ).

fof(c_0_1769,plain,
    ! [X86,X87] : ti(X86,ti(X86,X87)) = ti(X86,X87),
    inference(variable_rename,[status(thm)],[c_0_1161]) ).

fof(c_0_1770,plain,
    ! [X4] : ti(fun(X4,X4),combi(X4)) = combi(X4),
    inference(variable_rename,[status(thm)],[c_0_1162]) ).

fof(c_0_1771,plain,
    ! [X84,X85] :
      ( ~ finite_finite(X85)
      | ~ finite_finite(X84)
      | finite_finite(product_prod(X84,X85)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1163])]) ).

fof(c_0_1772,plain,
    ! [X84,X85] :
      ( ~ finite_finite(X85)
      | ~ finite_finite(X84)
      | finite_finite(sum_sum(X84,X85)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1164])]) ).

fof(c_0_1773,plain,
    ! [X84,X85] :
      ( ~ finite_finite(X85)
      | ~ finite_finite(X84)
      | finite_finite(fun(X84,X85)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1165])]) ).

fof(c_0_1774,plain,
    ! [X84,X85] :
      ( ~ ord(X85)
      | ord(fun(X84,X85)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1166])]) ).

fof(c_0_1775,plain,
    ! [X84,X85] :
      ( ~ top(X85)
      | top(fun(X84,X85)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1167])]) ).

fof(c_0_1776,plain,
    ! [X84,X85] :
      ( ~ order(X85)
      | order(fun(X84,X85)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1168])]) ).

fof(c_0_1777,plain,
    ! [X84,X85] :
      ( ~ preorder(X85)
      | preorder(fun(X84,X85)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1169])]) ).

fof(c_0_1778,axiom,
    ti(fun(arrow_660593299e_indi,nat),h) = h,
    c_0_1170 ).

fof(c_0_1779,axiom,
    ti(fun(bool,bool),fNot) = fNot,
    c_0_1171 ).

fof(c_0_1780,axiom,
    ti(fun(nat,nat),suc) = suc,
    c_0_1172 ).

fof(c_0_1781,plain,
    ! [X4] :
      ( ~ top(X4)
      | ti(X4,top_top(X4)) = top_top(X4) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1173])]) ).

fof(c_0_1782,plain,
    ! [X4] :
      ( ~ zero(X4)
      | ti(X4,zero_zero(X4)) = zero_zero(X4) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1174])]) ).

fof(c_0_1783,plain,
    ! [X4] :
      ( ~ one(X4)
      | ti(X4,one_one(X4)) = one_one(X4) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1175])]) ).

fof(c_0_1784,plain,
    ! [X87] :
      ( ti(bool,X87) = fTrue
      | ti(bool,X87) = fFalse ),
    inference(variable_rename,[status(thm)],[c_0_1176]) ).

fof(c_0_1785,plain,
    ! [X87] :
      ( ti(bool,X87) = fTrue
      | ti(bool,X87) = fFalse ),
    inference(variable_rename,[status(thm)],[c_0_1177]) ).

fof(c_0_1786,plain,
    ! [X4] : ti(X4,undefined(X4)) = undefined(X4),
    inference(variable_rename,[status(thm)],[c_0_1178]) ).

fof(c_0_1787,plain,
    ! [X4] :
      ( ~ zero_neq_one(X4)
      | one_one(X4) != zero_zero(X4) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1179])]) ).

fof(c_0_1788,plain,
    ! [X4] :
      ( ~ zero_neq_one(X4)
      | zero_zero(X4) != one_one(X4) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1180])]) ).

fof(c_0_1789,plain,
    ! [X84] :
      ( ~ finite_finite(X84)
      | finite_finite(option(X84)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1181])]) ).

fof(c_0_1790,axiom,
    ti(nat,n) = n,
    c_0_1182 ).

fof(c_0_1791,axiom,
    ti(arrow_490897120le_alt,e) = e,
    c_0_1183 ).

fof(c_0_1792,axiom,
    ti(arrow_490897120le_alt,b) = b,
    c_0_1184 ).

fof(c_0_1793,axiom,
    ti(arrow_490897120le_alt,a) = a,
    c_0_1185 ).

fof(c_0_1794,axiom,
    ti(bool,fTrue) = fTrue,
    c_0_1186 ).

fof(c_0_1795,axiom,
    ti(bool,fFalse) = fFalse,
    c_0_1187 ).

fof(c_0_1796,axiom,
    hBOOL(fTrue),
    c_0_1188 ).

fof(c_0_1797,axiom,
    finite_finite(product_unit),
    c_0_1189 ).

fof(c_0_1798,axiom,
    ord(bool),
    c_0_1190 ).

fof(c_0_1799,axiom,
    top(bool),
    c_0_1191 ).

fof(c_0_1800,axiom,
    order(bool),
    c_0_1192 ).

fof(c_0_1801,axiom,
    finite_finite(bool),
    c_0_1193 ).

fof(c_0_1802,axiom,
    preorder(bool),
    c_0_1194 ).

fof(c_0_1803,axiom,
    one(nat),
    c_0_1195 ).

fof(c_0_1804,axiom,
    zero(nat),
    c_0_1196 ).

fof(c_0_1805,axiom,
    ord(nat),
    c_0_1197 ).

fof(c_0_1806,axiom,
    order(nat),
    c_0_1198 ).

fof(c_0_1807,axiom,
    monoid_add(nat),
    c_0_1199 ).

fof(c_0_1808,axiom,
    linorder(nat),
    c_0_1200 ).

fof(c_0_1809,axiom,
    preorder(nat),
    c_0_1201 ).

fof(c_0_1810,axiom,
    zero_neq_one(nat),
    c_0_1202 ).

fof(c_0_1811,axiom,
    comm_semiring_1(nat),
    c_0_1203 ).

fof(c_0_1812,axiom,
    comm_monoid_add(nat),
    c_0_1204 ).

fof(c_0_1813,axiom,
    ab_semigroup_add(nat),
    c_0_1205 ).

fof(c_0_1814,axiom,
    linordered_semidom(nat),
    c_0_1206 ).

fof(c_0_1815,axiom,
    cancel_semigroup_add(nat),
    c_0_1207 ).

fof(c_0_1816,axiom,
    cancel146912293up_add(nat),
    c_0_1208 ).

fof(c_0_1817,axiom,
    ordere216010020id_add(nat),
    c_0_1209 ).

fof(c_0_1818,axiom,
    ordere779506340up_add(nat),
    c_0_1210 ).

fof(c_0_1819,axiom,
    ordere236663937imp_le(nat),
    c_0_1211 ).

fof(c_0_1820,axiom,
    ordere223160158up_add(nat),
    c_0_1212 ).

fof(c_0_1821,axiom,
    semiri456707255roduct(nat),
    c_0_1213 ).

fof(c_0_1822,axiom,
    a != b,
    c_0_1214 ).

fof(c_0_1823,axiom,
    c != d,
    c_0_1215 ).

cnf(c_0_1824,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))),lab)),lba))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))))) ),
    inference(split_conjunct,[status(thm)],[c_0_1216]) ).

cnf(c_0_1825,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),lab)),lba))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))))) ),
    inference(split_conjunct,[status(thm)],[c_0_1217]) ).

cnf(c_0_1826,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,p)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))))) ),
    inference(split_conjunct,[status(thm)],[c_0_1218]) ).

cnf(c_0_1827,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e))))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))),lab)),lba)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1216]) ).

cnf(c_0_1828,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e))))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),lab)),lba)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1217]) ).

cnf(c_0_1829,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e))))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,p))) ),
    inference(split_conjunct,[status(thm)],[c_0_1218]) ).

cnf(c_0_1830,plain,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))))),
    inference(split_conjunct,[status(thm)],[c_0_1219]) ).

cnf(c_0_1831,plain,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))))),
    inference(split_conjunct,[status(thm)],[c_0_1220]) ).

cnf(c_0_1832,plain,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))))),
    inference(split_conjunct,[status(thm)],[c_0_1221]) ).

cnf(c_0_1833,plain,
    hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))),arrow_1111136790e_Prof)),
    inference(split_conjunct,[status(thm)],[c_0_1222]) ).

cnf(c_0_1834,plain,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),esk28_0),one_one(nat))))),lab)),lba)))),
    inference(split_conjunct,[status(thm)],[c_0_1223]) ).

cnf(c_0_1835,plain,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),esk27_0),one_one(nat))))),lab)),lba)))),
    inference(split_conjunct,[status(thm)],[c_0_1224]) ).

cnf(c_0_1836,plain,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))),lab)),lba)))),
    inference(split_conjunct,[status(thm)],[c_0_1225]) ).

cnf(c_0_1837,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),X1))),lab)),lba))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),esk28_0)) ),
    inference(split_conjunct,[status(thm)],[c_0_1223]) ).

cnf(c_0_1838,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),X1))),lab)),lba))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),esk27_0)) ),
    inference(split_conjunct,[status(thm)],[c_0_1224]) ).

cnf(c_0_1839,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),X1))),lab)),lba))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),n)) ),
    inference(split_conjunct,[status(thm)],[c_0_1226]) ).

cnf(c_0_1840,plain,
    hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),X1))),lab)),lba)),arrow_1111136790e_Prof)),
    inference(split_conjunct,[status(thm)],[c_0_1227]) ).

cnf(c_0_1841,plain,
    ( hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(fun(product_prod(X1,X2),bool),fun(fun(product_prod(X1,X2),bool),bool),ord_less_eq(fun(product_prod(X1,X2),bool)),X3),X4))
    | ~ hBOOL(hAPP(fun(X1,fun(X2,bool)),bool,hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,fun(X2,bool)),bool),ord_less_eq(fun(X1,fun(X2,bool))),hAPP(fun(product_prod(X1,X2),bool),fun(X1,fun(X2,bool)),hAPP(fun(X1,fun(fun(product_prod(X1,X2),bool),fun(X2,bool))),fun(fun(product_prod(X1,X2),bool),fun(X1,fun(X2,bool))),combc(X1,fun(product_prod(X1,X2),bool),fun(X2,bool)),hAPP(fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),fun(X1,fun(fun(product_prod(X1,X2),bool),fun(X2,bool))),hAPP(fun(fun(X2,fun(fun(product_prod(X1,X2),bool),bool)),fun(fun(product_prod(X1,X2),bool),fun(X2,bool))),fun(fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),fun(X1,fun(fun(product_prod(X1,X2),bool),fun(X2,bool)))),combb(fun(X2,fun(fun(product_prod(X1,X2),bool),bool)),fun(fun(product_prod(X1,X2),bool),fun(X2,bool)),X1),combc(X2,fun(product_prod(X1,X2),bool),bool)),hAPP(fun(X1,fun(X2,product_prod(X1,X2))),fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),hAPP(fun(fun(X2,product_prod(X1,X2)),fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),fun(fun(X1,fun(X2,product_prod(X1,X2))),fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool)))),combb(fun(X2,product_prod(X1,X2)),fun(X2,fun(fun(product_prod(X1,X2),bool),bool)),X1),hAPP(fun(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool)),fun(fun(X2,product_prod(X1,X2)),fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),combb(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),X2),member(product_prod(X1,X2)))),product_Pair(X1,X2)))),X3)),hAPP(fun(product_prod(X1,X2),bool),fun(X1,fun(X2,bool)),hAPP(fun(X1,fun(fun(product_prod(X1,X2),bool),fun(X2,bool))),fun(fun(product_prod(X1,X2),bool),fun(X1,fun(X2,bool))),combc(X1,fun(product_prod(X1,X2),bool),fun(X2,bool)),hAPP(fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),fun(X1,fun(fun(product_prod(X1,X2),bool),fun(X2,bool))),hAPP(fun(fun(X2,fun(fun(product_prod(X1,X2),bool),bool)),fun(fun(product_prod(X1,X2),bool),fun(X2,bool))),fun(fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),fun(X1,fun(fun(product_prod(X1,X2),bool),fun(X2,bool)))),combb(fun(X2,fun(fun(product_prod(X1,X2),bool),bool)),fun(fun(product_prod(X1,X2),bool),fun(X2,bool)),X1),combc(X2,fun(product_prod(X1,X2),bool),bool)),hAPP(fun(X1,fun(X2,product_prod(X1,X2))),fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),hAPP(fun(fun(X2,product_prod(X1,X2)),fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),fun(fun(X1,fun(X2,product_prod(X1,X2))),fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool)))),combb(fun(X2,product_prod(X1,X2)),fun(X2,fun(fun(product_prod(X1,X2),bool),bool)),X1),hAPP(fun(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool)),fun(fun(X2,product_prod(X1,X2)),fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),combb(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),X2),member(product_prod(X1,X2)))),product_Pair(X1,X2)))),X4))) ),
    inference(split_conjunct,[status(thm)],[c_0_1228]) ).

cnf(c_0_1842,plain,
    ( hBOOL(hAPP(fun(X1,fun(X2,bool)),bool,hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,fun(X2,bool)),bool),ord_less_eq(fun(X1,fun(X2,bool))),hAPP(fun(product_prod(X1,X2),bool),fun(X1,fun(X2,bool)),hAPP(fun(X1,fun(fun(product_prod(X1,X2),bool),fun(X2,bool))),fun(fun(product_prod(X1,X2),bool),fun(X1,fun(X2,bool))),combc(X1,fun(product_prod(X1,X2),bool),fun(X2,bool)),hAPP(fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),fun(X1,fun(fun(product_prod(X1,X2),bool),fun(X2,bool))),hAPP(fun(fun(X2,fun(fun(product_prod(X1,X2),bool),bool)),fun(fun(product_prod(X1,X2),bool),fun(X2,bool))),fun(fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),fun(X1,fun(fun(product_prod(X1,X2),bool),fun(X2,bool)))),combb(fun(X2,fun(fun(product_prod(X1,X2),bool),bool)),fun(fun(product_prod(X1,X2),bool),fun(X2,bool)),X1),combc(X2,fun(product_prod(X1,X2),bool),bool)),hAPP(fun(X1,fun(X2,product_prod(X1,X2))),fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),hAPP(fun(fun(X2,product_prod(X1,X2)),fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),fun(fun(X1,fun(X2,product_prod(X1,X2))),fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool)))),combb(fun(X2,product_prod(X1,X2)),fun(X2,fun(fun(product_prod(X1,X2),bool),bool)),X1),hAPP(fun(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool)),fun(fun(X2,product_prod(X1,X2)),fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),combb(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),X2),member(product_prod(X1,X2)))),product_Pair(X1,X2)))),X3)),hAPP(fun(product_prod(X1,X2),bool),fun(X1,fun(X2,bool)),hAPP(fun(X1,fun(fun(product_prod(X1,X2),bool),fun(X2,bool))),fun(fun(product_prod(X1,X2),bool),fun(X1,fun(X2,bool))),combc(X1,fun(product_prod(X1,X2),bool),fun(X2,bool)),hAPP(fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),fun(X1,fun(fun(product_prod(X1,X2),bool),fun(X2,bool))),hAPP(fun(fun(X2,fun(fun(product_prod(X1,X2),bool),bool)),fun(fun(product_prod(X1,X2),bool),fun(X2,bool))),fun(fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),fun(X1,fun(fun(product_prod(X1,X2),bool),fun(X2,bool)))),combb(fun(X2,fun(fun(product_prod(X1,X2),bool),bool)),fun(fun(product_prod(X1,X2),bool),fun(X2,bool)),X1),combc(X2,fun(product_prod(X1,X2),bool),bool)),hAPP(fun(X1,fun(X2,product_prod(X1,X2))),fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),hAPP(fun(fun(X2,product_prod(X1,X2)),fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),fun(fun(X1,fun(X2,product_prod(X1,X2))),fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool)))),combb(fun(X2,product_prod(X1,X2)),fun(X2,fun(fun(product_prod(X1,X2),bool),bool)),X1),hAPP(fun(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool)),fun(fun(X2,product_prod(X1,X2)),fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),combb(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),X2),member(product_prod(X1,X2)))),product_Pair(X1,X2)))),X4)))
    | ~ hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(fun(product_prod(X1,X2),bool),fun(fun(product_prod(X1,X2),bool),bool),ord_less_eq(fun(product_prod(X1,X2),bool)),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_1228]) ).

cnf(c_0_1843,plain,
    ( hAPP(nat,nat,suc,hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),hAPP(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool)),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool))),combb(nat,fun(fun(nat,bool),bool),nat),member(nat)),suc)),X1))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X2))))) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),X1))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,X2)))))
    | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_1229]) ).

cnf(c_0_1844,plain,
    ( hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),hAPP(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool)),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool))),combb(nat,fun(fun(nat,bool),bool),nat),member(nat)),suc)),X1))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X2)))) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),X1))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,X2)))))
    | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_1230]) ).

cnf(c_0_1845,plain,
    ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6))
    | ~ order(X1)
    | ~ order(X2)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X5,X4)),X6))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,esk58_6(X1,X2,X5,X6,X3,X4))),hAPP(X1,X2,X5,esk59_6(X1,X2,X5,X6,X3,X4)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1231]) ).

cnf(c_0_1846,plain,
    ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6))
    | ~ order(X1)
    | ~ order(X2)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X4)),X6))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X5,esk48_6(X1,X2,X5,X6,X3,X4))),hAPP(X1,X2,X5,esk49_6(X1,X2,X5,X6,X3,X4)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1232]) ).

cnf(c_0_1847,plain,
    ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5))
    | ~ order(X1)
    | ~ order(X2)
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X4)),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X4))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,esk43_6(X1,X2,X6,X3,X4,X5))),hAPP(X1,X2,X3,esk42_6(X1,X2,X6,X3,X4,X5)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1233]) ).

cnf(c_0_1848,plain,
    ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5))
    | ~ ord(X1)
    | ~ order(X2)
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,X4)),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X4))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,esk41_6(X1,X2,X6,X3,X4,X5))),hAPP(X1,X2,X3,esk40_6(X1,X2,X6,X3,X4,X5)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1234]) ).

cnf(c_0_1849,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4)))
    | ~ order(X1)
    | ~ order(X2)
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X3),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X3)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X6,esk57_6(X1,X2,X5,X6,X3,X4))),hAPP(X2,X1,X6,esk56_6(X1,X2,X5,X6,X3,X4)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1235]) ).

cnf(c_0_1850,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4)))
    | ~ order(X1)
    | ~ order(X2)
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X3),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),hAPP(X2,X1,X6,X3)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X6,esk55_6(X1,X2,X5,X6,X3,X4))),hAPP(X2,X1,X6,esk54_6(X1,X2,X5,X6,X3,X4)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1236]) ).

cnf(c_0_1851,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6)))
    | ~ order(X1)
    | ~ order(X2)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X5)))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X5),X6))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X4,esk46_6(X1,X2,X6,X3,X4,X5))),hAPP(X2,X1,X4,esk47_6(X1,X2,X6,X3,X4,X5)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1237]) ).

cnf(c_0_1852,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6)))
    | ~ order(X1)
    | ~ order(X2)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),hAPP(X2,X1,X4,X5)))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X5),X6))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X4,esk44_6(X1,X2,X6,X3,X4,X5))),hAPP(X2,X1,X4,esk45_6(X1,X2,X6,X3,X4,X5)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1238]) ).

cnf(c_0_1853,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,esk2_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,esk2_6(X6,X5,X3,X4,X1,X2)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1239]) ).

cnf(c_0_1854,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,esk1_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,esk1_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(split_conjunct,[status(thm)],[c_0_1240]) ).

cnf(c_0_1855,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,esk1_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,esk1_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6))) ),
    inference(split_conjunct,[status(thm)],[c_0_1240]) ).

cnf(c_0_1856,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,esk4_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,esk4_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(split_conjunct,[status(thm)],[c_0_1241]) ).

cnf(c_0_1857,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,esk4_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,esk4_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6))) ),
    inference(split_conjunct,[status(thm)],[c_0_1241]) ).

cnf(c_0_1858,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,esk2_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,esk2_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(split_conjunct,[status(thm)],[c_0_1239]) ).

cnf(c_0_1859,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,esk1_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,esk1_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(split_conjunct,[status(thm)],[c_0_1240]) ).

cnf(c_0_1860,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,esk1_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,esk1_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6))) ),
    inference(split_conjunct,[status(thm)],[c_0_1240]) ).

cnf(c_0_1861,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,esk4_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,esk4_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(split_conjunct,[status(thm)],[c_0_1241]) ).

cnf(c_0_1862,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,esk4_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,esk4_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6))) ),
    inference(split_conjunct,[status(thm)],[c_0_1241]) ).

cnf(c_0_1863,plain,
    ( hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),X1))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,X2))))) != zero_zero(nat)
    | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_1242]) ).

cnf(c_0_1864,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1243]) ).

cnf(c_0_1865,plain,
    ( hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,X1),X2))
    | ~ hBOOL(hAPP(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1111136790e_Prof),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_2064824852le_Lin))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),esk24_2(X2,X1)),esk25_2(X2,X1))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,esk23_2(X2,X1)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1244]) ).

cnf(c_0_1866,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[c_0_1243]) ).

cnf(c_0_1867,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(split_conjunct,[status(thm)],[c_0_1245]) ).

cnf(c_0_1868,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[c_0_1245]) ).

cnf(c_0_1869,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[c_0_1246]) ).

cnf(c_0_1870,plain,
    ( hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,X1),X2))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),esk24_2(X2,X1)),esk25_2(X2,X1))),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),esk23_2(X2,X1),X2)))
    | ~ hBOOL(hAPP(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1111136790e_Prof),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_2064824852le_Lin)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1244]) ).

cnf(c_0_1871,plain,
    ( hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,X1),X2))
    | hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),esk23_2(X2,X1)),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1111136790e_Prof),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_2064824852le_Lin)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1244]) ).

cnf(c_0_1872,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X3)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X2),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,esk9_5(X1,X2,X3,X4,X5))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X2,esk9_5(X1,X2,X3,X4,X5))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_1247]) ).

cnf(c_0_1873,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X2)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X2),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,esk9_5(X1,X2,X3,X4,X5))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X2,esk9_5(X1,X2,X3,X4,X5))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X3))) ),
    inference(split_conjunct,[status(thm)],[c_0_1247]) ).

cnf(c_0_1874,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,esk3_5(X5,X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,esk3_5(X5,X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4))) ),
    inference(split_conjunct,[status(thm)],[c_0_1248]) ).

cnf(c_0_1875,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,esk3_5(X5,X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,esk3_5(X5,X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(split_conjunct,[status(thm)],[c_0_1248]) ).

cnf(c_0_1876,plain,
    ( hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,X1),X2))
    | ~ hBOOL(hAPP(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1111136790e_Prof),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_2064824852le_Lin))))
    | ti(arrow_490897120le_alt,esk24_2(X2,X1)) != ti(arrow_490897120le_alt,esk25_2(X2,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_1244]) ).

cnf(c_0_1877,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1243]) ).

cnf(c_0_1878,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1243]) ).

cnf(c_0_1879,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fdisj),X2)),X3)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1249]) ).

cnf(c_0_1880,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X3)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fdisj),X2)),X3)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1249]) ).

cnf(c_0_1881,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[c_0_1243]) ).

cnf(c_0_1882,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(split_conjunct,[status(thm)],[c_0_1245]) ).

cnf(c_0_1883,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(split_conjunct,[status(thm)],[c_0_1243]) ).

cnf(c_0_1884,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[c_0_1245]) ).

cnf(c_0_1885,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(split_conjunct,[status(thm)],[c_0_1245]) ).

cnf(c_0_1886,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[c_0_1246]) ).

cnf(c_0_1887,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(split_conjunct,[status(thm)],[c_0_1245]) ).

cnf(c_0_1888,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(split_conjunct,[status(thm)],[c_0_1246]) ).

cnf(c_0_1889,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,esk9_5(X1,X2,X3,X4,X5))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X2,esk9_5(X1,X2,X3,X4,X5))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X3)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X2),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_1247]) ).

cnf(c_0_1890,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,esk9_5(X1,X2,X3,X4,X5))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X2,esk9_5(X1,X2,X3,X4,X5))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X2)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X2),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X3))) ),
    inference(split_conjunct,[status(thm)],[c_0_1247]) ).

cnf(c_0_1891,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,esk3_5(X5,X4,X3,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,esk3_5(X5,X4,X3,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4))) ),
    inference(split_conjunct,[status(thm)],[c_0_1248]) ).

cnf(c_0_1892,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,esk3_5(X5,X4,X3,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,esk3_5(X5,X4,X3,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(split_conjunct,[status(thm)],[c_0_1248]) ).

cnf(c_0_1893,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,esk5_4(X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,esk5_4(X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3))) ),
    inference(split_conjunct,[status(thm)],[c_0_1250]) ).

cnf(c_0_1894,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,esk5_4(X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,esk5_4(X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4))) ),
    inference(split_conjunct,[status(thm)],[c_0_1250]) ).

cnf(c_0_1895,plain,
    ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),esk58_6(X1,X2,X5,X6,X3,X4)),esk59_6(X1,X2,X5,X6,X3,X4)))
    | ~ order(X1)
    | ~ order(X2)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X5,X4)),X6)) ),
    inference(split_conjunct,[status(thm)],[c_0_1231]) ).

cnf(c_0_1896,plain,
    ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),esk48_6(X1,X2,X5,X6,X3,X4)),esk49_6(X1,X2,X5,X6,X3,X4)))
    | ~ order(X1)
    | ~ order(X2)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X4)),X6)) ),
    inference(split_conjunct,[status(thm)],[c_0_1232]) ).

cnf(c_0_1897,plain,
    ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),esk43_6(X1,X2,X6,X3,X4,X5)),esk42_6(X1,X2,X6,X3,X4,X5)))
    | ~ order(X1)
    | ~ order(X2)
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X4)),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_1233]) ).

cnf(c_0_1898,plain,
    ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),esk41_6(X1,X2,X6,X3,X4,X5)),esk40_6(X1,X2,X6,X3,X4,X5)))
    | ~ ord(X1)
    | ~ order(X2)
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,X4)),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_1234]) ).

cnf(c_0_1899,plain,
    hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),X1)),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X2))))),
    inference(split_conjunct,[status(thm)],[c_0_1251]) ).

cnf(c_0_1900,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4)))
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),esk57_6(X1,X2,X5,X6,X3,X4)),esk56_6(X1,X2,X5,X6,X3,X4)))
    | ~ order(X1)
    | ~ order(X2)
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X3),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X3))) ),
    inference(split_conjunct,[status(thm)],[c_0_1235]) ).

cnf(c_0_1901,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4)))
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),esk55_6(X1,X2,X5,X6,X3,X4)),esk54_6(X1,X2,X5,X6,X3,X4)))
    | ~ order(X1)
    | ~ order(X2)
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X3),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),hAPP(X2,X1,X6,X3))) ),
    inference(split_conjunct,[status(thm)],[c_0_1236]) ).

cnf(c_0_1902,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6)))
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),esk46_6(X1,X2,X6,X3,X4,X5)),esk47_6(X1,X2,X6,X3,X4,X5)))
    | ~ order(X1)
    | ~ order(X2)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X5)))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X5),X6)) ),
    inference(split_conjunct,[status(thm)],[c_0_1237]) ).

cnf(c_0_1903,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6)))
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),esk44_6(X1,X2,X6,X3,X4,X5)),esk45_6(X1,X2,X6,X3,X4,X5)))
    | ~ order(X1)
    | ~ order(X2)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),hAPP(X2,X1,X4,X5)))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X5),X6)) ),
    inference(split_conjunct,[status(thm)],[c_0_1238]) ).

cnf(c_0_1904,plain,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1243]) ).

cnf(c_0_1905,plain,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[c_0_1243]) ).

cnf(c_0_1906,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1243]) ).

cnf(c_0_1907,plain,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(split_conjunct,[status(thm)],[c_0_1245]) ).

cnf(c_0_1908,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,esk5_4(X4,X3,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,esk5_4(X4,X3,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3))) ),
    inference(split_conjunct,[status(thm)],[c_0_1250]) ).

cnf(c_0_1909,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,esk5_4(X4,X3,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,esk5_4(X4,X3,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4))) ),
    inference(split_conjunct,[status(thm)],[c_0_1250]) ).

cnf(c_0_1910,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X5)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1252]) ).

cnf(c_0_1911,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X1)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1253]) ).

cnf(c_0_1912,plain,
    ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(fun(X1,X2),bool),fun(fun(fun(X1,X2),bool),bool),ord_less_eq(fun(fun(X1,X2),bool)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X3),X4)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X3),X5)))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),hAPP(X1,fun(X2,bool),X4,esk52_5(X2,X1,X4,X5,X3))),hAPP(X1,fun(X2,bool),X5,esk52_5(X2,X1,X4,X5,X3)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1254]) ).

cnf(c_0_1913,plain,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[c_0_1245]) ).

cnf(c_0_1914,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(split_conjunct,[status(thm)],[c_0_1243]) ).

cnf(c_0_1915,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk67_6(X2,X1,X3,X4,X5,X6)),X6))
    | hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X5),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X6),X3)))
    | ~ hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X4),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X6),X3))) ),
    inference(split_conjunct,[status(thm)],[c_0_1255]) ).

cnf(c_0_1916,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk67_6(X2,X1,X3,X4,X5,X6)),X6))
    | hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X4),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X6),X3)))
    | ~ hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X5),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X6),X3))) ),
    inference(split_conjunct,[status(thm)],[c_0_1255]) ).

cnf(c_0_1917,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[c_0_1246]) ).

cnf(c_0_1918,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(split_conjunct,[status(thm)],[c_0_1245]) ).

cnf(c_0_1919,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fdisj),X2)),X3))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X3)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_1249]) ).

cnf(c_0_1920,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(split_conjunct,[status(thm)],[c_0_1245]) ).

cnf(c_0_1921,plain,
    ( ti(fun(product_prod(X1,X2),bool),X3) = ti(fun(product_prod(X1,X2),bool),X4)
    | ~ hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),member(product_prod(X1,X2)),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),esk21_4(X1,X2,X4,X3)),esk22_4(X1,X2,X4,X3))),X4))
    | ~ hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),member(product_prod(X1,X2)),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),esk21_4(X1,X2,X4,X3)),esk22_4(X1,X2,X4,X3))),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1256]) ).

cnf(c_0_1922,plain,
    hBOOL(hAPP(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),f),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1111136790e_Prof),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_2064824852le_Lin)))),
    inference(split_conjunct,[status(thm)],[c_0_1257]) ).

cnf(c_0_1923,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(split_conjunct,[status(thm)],[c_0_1243]) ).

cnf(c_0_1924,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(split_conjunct,[status(thm)],[c_0_1245]) ).

cnf(c_0_1925,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(split_conjunct,[status(thm)],[c_0_1246]) ).

cnf(c_0_1926,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X2)),X3))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_1258]) ).

cnf(c_0_1927,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X2)),X3))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X3))) ),
    inference(split_conjunct,[status(thm)],[c_0_1258]) ).

cnf(c_0_1928,plain,
    ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less_eq(nat)),X1)),X2))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),esk77_2(X2,X1)),hAPP(nat,nat,X1,esk77_2(X2,X1)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1259]) ).

cnf(c_0_1929,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(split_conjunct,[status(thm)],[c_0_1243]) ).

cnf(c_0_1930,plain,
    ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X3),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X4),X5)))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X3,esk68_5(X2,X1,X3,X5,X4))),hAPP(X1,fun(X2,bool),X5,esk68_5(X2,X1,X3,X5,X4)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1260]) ).

cnf(c_0_1931,plain,
    ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X3),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X4),X5)))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X3,esk33_5(X2,X1,X3,X5,X4))),hAPP(X1,fun(X2,bool),X5,esk33_5(X2,X1,X3,X5,X4)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1261]) ).

cnf(c_0_1932,plain,
    ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X5),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X6),X4)))
    | hAPP(X1,X2,X3,esk67_6(X2,X1,X4,X3,X5,X6)) != hAPP(X1,X2,X5,esk67_6(X2,X1,X4,X3,X5,X6))
    | ~ hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X3),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X6),X4))) ),
    inference(split_conjunct,[status(thm)],[c_0_1255]) ).

cnf(c_0_1933,plain,
    ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X3),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X6),X4)))
    | hAPP(X1,X2,X3,esk67_6(X2,X1,X4,X3,X5,X6)) != hAPP(X1,X2,X5,esk67_6(X2,X1,X4,X3,X5,X6))
    | ~ hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X5),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X6),X4))) ),
    inference(split_conjunct,[status(thm)],[c_0_1255]) ).

cnf(c_0_1934,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1252]) ).

cnf(c_0_1935,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X5)),X3))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1252]) ).

cnf(c_0_1936,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1253]) ).

cnf(c_0_1937,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X1)),X3))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1253]) ).

cnf(c_0_1938,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X5)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1252]) ).

cnf(c_0_1939,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1252]) ).

cnf(c_0_1940,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X1)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1253]) ).

cnf(c_0_1941,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1253]) ).

cnf(c_0_1942,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(split_conjunct,[status(thm)],[c_0_1243]) ).

cnf(c_0_1943,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(split_conjunct,[status(thm)],[c_0_1245]) ).

cnf(c_0_1944,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
    | ~ linordered_idom(X1)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),ring_1_Ints(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),one_one(X1)),X2)),X2)),zero_zero(X1))) ),
    inference(split_conjunct,[status(thm)],[c_0_1262]) ).

cnf(c_0_1945,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(split_conjunct,[status(thm)],[c_0_1245]) ).

cnf(c_0_1946,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1243]) ).

cnf(c_0_1947,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(split_conjunct,[status(thm)],[c_0_1243]) ).

cnf(c_0_1948,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(split_conjunct,[status(thm)],[c_0_1245]) ).

cnf(c_0_1949,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(split_conjunct,[status(thm)],[c_0_1246]) ).

cnf(c_0_1950,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(split_conjunct,[status(thm)],[c_0_1243]) ).

cnf(c_0_1951,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1243]) ).

cnf(c_0_1952,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba)) ),
    inference(split_conjunct,[status(thm)],[c_0_1243]) ).

cnf(c_0_1953,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba)) ),
    inference(split_conjunct,[status(thm)],[c_0_1245]) ).

cnf(c_0_1954,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X5)),X3))
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1252]) ).

cnf(c_0_1955,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X1)),X3))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1253]) ).

cnf(c_0_1956,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_1252]) ).

cnf(c_0_1957,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3))
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_1253]) ).

cnf(c_0_1958,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1252]) ).

cnf(c_0_1959,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1253]) ).

cnf(c_0_1960,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(split_conjunct,[status(thm)],[c_0_1243]) ).

cnf(c_0_1961,plain,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1243]) ).

cnf(c_0_1962,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(split_conjunct,[status(thm)],[c_0_1245]) ).

cnf(c_0_1963,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[c_0_1243]) ).

cnf(c_0_1964,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(split_conjunct,[status(thm)],[c_0_1243]) ).

cnf(c_0_1965,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(split_conjunct,[status(thm)],[c_0_1245]) ).

cnf(c_0_1966,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(split_conjunct,[status(thm)],[c_0_1245]) ).

cnf(c_0_1967,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1243]) ).

cnf(c_0_1968,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),X2,hAPP(fun(X3,bool),X1,X4,X5)),hAPP(fun(X3,bool),X1,X4,X6)) = hAPP(fun(X3,bool),X1,X4,X6)
    | ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X5),X6))
    | ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X6))
    | ~ hBOOL(hAPP(fun(fun(X3,bool),X1),bool,hAPP(fun(X3,X1),fun(fun(fun(X3,bool),X1),bool),hAPP(X1,fun(fun(X3,X1),fun(fun(fun(X3,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X3,X1),fun(fun(fun(X3,bool),X1),bool))),finite908156982e_idem(X1,X3),X2),X7),X8),X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_1263]) ).

cnf(c_0_1969,plain,
    ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X3),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X4),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),X5))))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X3,esk65_5(X2,X1,X3,X5,X4))),X5)) ),
    inference(split_conjunct,[status(thm)],[c_0_1264]) ).

cnf(c_0_1970,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),X2,hAPP(X3,X1,X4,X5)),hAPP(fun(X3,bool),X1,X6,X7)) = hAPP(fun(X3,bool),X1,X6,X7)
    | ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X5),X7))
    | ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X7))
    | ~ hBOOL(hAPP(fun(fun(X3,bool),X1),bool,hAPP(fun(X3,X1),fun(fun(fun(X3,bool),X1),bool),hAPP(X1,fun(fun(X3,X1),fun(fun(fun(X3,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X3,X1),fun(fun(fun(X3,bool),X1),bool))),finite908156982e_idem(X1,X3),X2),X8),X4),X6)) ),
    inference(split_conjunct,[status(thm)],[c_0_1265]) ).

cnf(c_0_1971,plain,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(split_conjunct,[status(thm)],[c_0_1243]) ).

cnf(c_0_1972,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[c_0_1245]) ).

cnf(c_0_1973,plain,
    ( hAPP(fun(X1,bool),nat,finite_card(X1),X2) = hAPP(fun(X3,bool),nat,finite_card(X3),X4)
    | ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X5),X4))
    | ~ hBOOL(hAPP(fun(fun(X3,X1),bool),bool,hAPP(fun(X3,X1),fun(fun(fun(X3,X1),bool),bool),member(fun(X3,X1)),X5),hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool)),pi(X3,X1),X4),hAPP(fun(X1,bool),fun(X3,fun(X1,bool)),combk(fun(X1,bool),X3),X2))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X6),X2))
    | ~ hBOOL(hAPP(fun(fun(X1,X3),bool),bool,hAPP(fun(X1,X3),fun(fun(fun(X1,X3),bool),bool),member(fun(X1,X3)),X6),hAPP(fun(X1,fun(X3,bool)),fun(fun(X1,X3),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X3,bool)),fun(fun(X1,X3),bool)),pi(X1,X3),X2),hAPP(fun(X3,bool),fun(X1,fun(X3,bool)),combk(fun(X3,bool),X1),X4)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1266]) ).

cnf(c_0_1974,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(split_conjunct,[status(thm)],[c_0_1246]) ).

cnf(c_0_1975,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(split_conjunct,[status(thm)],[c_0_1243]) ).

cnf(c_0_1976,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(split_conjunct,[status(thm)],[c_0_1245]) ).

cnf(c_0_1977,plain,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(split_conjunct,[status(thm)],[c_0_1245]) ).

cnf(c_0_1978,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(split_conjunct,[status(thm)],[c_0_1245]) ).

cnf(c_0_1979,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1252]) ).

cnf(c_0_1980,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1253]) ).

cnf(c_0_1981,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1252]) ).

cnf(c_0_1982,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X5)),X3))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1252]) ).

cnf(c_0_1983,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1252]) ).

cnf(c_0_1984,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1253]) ).

cnf(c_0_1985,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X1)),X3))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1253]) ).

cnf(c_0_1986,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1253]) ).

cnf(c_0_1987,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1252]) ).

cnf(c_0_1988,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1253]) ).

cnf(c_0_1989,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1252]) ).

cnf(c_0_1990,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1253]) ).

cnf(c_0_1991,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(split_conjunct,[status(thm)],[c_0_1246]) ).

cnf(c_0_1992,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba)) ),
    inference(split_conjunct,[status(thm)],[c_0_1243]) ).

cnf(c_0_1993,plain,
    ( ti(fun(product_prod(X1,X2),bool),X3) = ti(fun(product_prod(X1,X2),bool),X4)
    | hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),member(product_prod(X1,X2)),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),esk21_4(X1,X2,X4,X3)),esk22_4(X1,X2,X4,X3))),X4))
    | hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),member(product_prod(X1,X2)),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),esk21_4(X1,X2,X4,X3)),esk22_4(X1,X2,X4,X3))),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1256]) ).

cnf(c_0_1994,plain,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(split_conjunct,[status(thm)],[c_0_1245]) ).

cnf(c_0_1995,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,X4)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,esk14_4(X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1267]) ).

cnf(c_0_1996,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(split_conjunct,[status(thm)],[c_0_1245]) ).

cnf(c_0_1997,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X5) ),
    inference(split_conjunct,[status(thm)],[c_0_1252]) ).

cnf(c_0_1998,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X5) ),
    inference(split_conjunct,[status(thm)],[c_0_1253]) ).

cnf(c_0_1999,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(split_conjunct,[status(thm)],[c_0_1245]) ).

cnf(c_0_2000,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),X2,X3),X3) = ti(X1,X3)
    | ~ hBOOL(hAPP(fun(fun(X4,bool),X1),bool,hAPP(fun(X4,X1),fun(fun(fun(X4,bool),X1),bool),hAPP(X1,fun(fun(X4,X1),fun(fun(fun(X4,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X4,X1),fun(fun(fun(X4,bool),X1),bool))),finite908156982e_idem(X1,X4),X2),X5),X6),X7)) ),
    inference(split_conjunct,[status(thm)],[c_0_1268]) ).

cnf(c_0_2001,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(split_conjunct,[status(thm)],[c_0_1246]) ).

cnf(c_0_2002,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(split_conjunct,[status(thm)],[c_0_1246]) ).

cnf(c_0_2003,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba)) ),
    inference(split_conjunct,[status(thm)],[c_0_1245]) ).

cnf(c_0_2004,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(split_conjunct,[status(thm)],[c_0_1243]) ).

cnf(c_0_2005,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1))) ),
    inference(split_conjunct,[status(thm)],[c_0_1246]) ).

cnf(c_0_2006,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1243]) ).

cnf(c_0_2007,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),one_one(X1)),X2)),X2)),zero_zero(X1)))
    | ~ linordered_idom(X1)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),ring_1_Ints(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1))) ),
    inference(split_conjunct,[status(thm)],[c_0_1262]) ).

cnf(c_0_2008,plain,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X2,bool),nat,finite_card(X2),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X4))),hAPP(fun(X1,bool),nat,finite_card(X1),X4))) ),
    inference(split_conjunct,[status(thm)],[c_0_1269]) ).

cnf(c_0_2009,plain,
    ( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X1),X2),X3)),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X1),arrow_2064824852le_Lin)) ),
    inference(split_conjunct,[status(thm)],[c_0_1270]) ).

cnf(c_0_2010,plain,
    ( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X1),X2),X3)),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X1),arrow_2064824852le_Lin)) ),
    inference(split_conjunct,[status(thm)],[c_0_1271]) ).

cnf(c_0_2011,plain,
    ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),esk12_1(X1)),esk13_1(X1))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,esk11_1(X1))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),esk12_1(X1)),esk13_1(X1))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,esk10_1(X1)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1247]) ).

cnf(c_0_2012,plain,
    ( ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X1),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),X1))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X2)),X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_1272]) ).

cnf(c_0_2013,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin)) ),
    inference(split_conjunct,[status(thm)],[c_0_1273]) ).

cnf(c_0_2014,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(X1,bool)),combc(X1,fun(X1,bool),bool),member(X1)),X2)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(X1,bool)),combc(X1,fun(X1,bool),bool),member(X1)),X3))) ),
    inference(split_conjunct,[status(thm)],[c_0_1274]) ).

cnf(c_0_2015,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),hAPP(fun(X2,X3),fun(X2,X1),hAPP(fun(X3,X1),fun(fun(X2,X3),fun(X2,X1)),combb(X3,X1,X2),X4),X5)),top_top(fun(X2,bool)))))
    | ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),hAPP(fun(X2,bool),fun(X3,bool),hAPP(fun(X2,X3),fun(fun(X2,bool),fun(X3,bool)),image(X2,X3),X5),top_top(fun(X2,bool))))) ),
    inference(split_conjunct,[status(thm)],[c_0_1275]) ).

cnf(c_0_2016,plain,
    ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(fun(X1,X2),bool),fun(fun(fun(X1,X2),bool),bool),ord_less_eq(fun(fun(X1,X2),bool)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X3),X4)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X3),X5)))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk52_5(X2,X1,X4,X5,X3)),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1254]) ).

cnf(c_0_2017,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(split_conjunct,[status(thm)],[c_0_1245]) ).

cnf(c_0_2018,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X4)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X3),X4))) ),
    inference(split_conjunct,[status(thm)],[c_0_1276]) ).

cnf(c_0_2019,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X3),X4))) ),
    inference(split_conjunct,[status(thm)],[c_0_1277]) ).

cnf(c_0_2020,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(split_conjunct,[status(thm)],[c_0_1245]) ).

cnf(c_0_2021,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X2,X1,hAPP(fun(X1,X2),fun(X2,X1),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)),hilbert_inv_into(X1,X2),X3),X4),X5)),X3))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X5),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X4),X3))) ),
    inference(split_conjunct,[status(thm)],[c_0_1278]) ).

cnf(c_0_2022,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,X1,X2)),X3)),hAPP(nat,nat,X1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,X1,esk61_3(X2,X3,X1))),hAPP(nat,nat,X1,esk62_3(X2,X3,X1)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1279]) ).

cnf(c_0_2023,plain,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,hAPP(nat,arrow_660593299e_indi,hAPP(fun(arrow_660593299e_indi,nat),fun(nat,arrow_660593299e_indi),hAPP(fun(arrow_660593299e_indi,bool),fun(fun(arrow_660593299e_indi,nat),fun(nat,arrow_660593299e_indi)),hilbert_inv_into(arrow_660593299e_indi,nat),top_top(fun(arrow_660593299e_indi,bool))),h),n)))),
    inference(split_conjunct,[status(thm)],[c_0_1280]) ).

cnf(c_0_2024,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X4))
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,X2,esk91_4(X1,X3,X4,X2))),hAPP(nat,X1,X2,hAPP(nat,nat,suc,esk91_4(X1,X3,X4,X2)))))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,X2,X3)),hAPP(nat,X1,X2,X4))) ),
    inference(split_conjunct,[status(thm)],[c_0_1281]) ).

cnf(c_0_2025,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X4)),X5))
    | ~ hBOOL(hAPP(fun(fun(X2,X1),bool),bool,hAPP(fun(X2,X1),fun(fun(fun(X2,X1),bool),bool),member(fun(X2,X1)),X3),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,X1),bool),hAPP(fun(X2,bool),fun(fun(X2,fun(X1,bool)),fun(fun(X2,X1),bool)),pi(X2,X1),X4),hAPP(fun(X1,bool),fun(X2,fun(X1,bool)),combk(fun(X1,bool),X2),X5)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1282]) ).

cnf(c_0_2026,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1252]) ).

cnf(c_0_2027,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1253]) ).

cnf(c_0_2028,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1252]) ).

cnf(c_0_2029,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1253]) ).

cnf(c_0_2030,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1252]) ).

cnf(c_0_2031,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1253]) ).

cnf(c_0_2032,plain,
    ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),esk12_1(X1)),esk13_1(X1))),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),esk11_1(X1),X2)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),esk12_1(X1)),esk13_1(X1))),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),esk10_1(X1),X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_1247]) ).

cnf(c_0_2033,plain,
    ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),esk12_1(X1)),esk13_1(X1))),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),esk10_1(X1),X2)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),esk12_1(X1)),esk13_1(X1))),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),esk11_1(X1),X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_1247]) ).

cnf(c_0_2034,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X3),X4)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X4)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1276]) ).

cnf(c_0_2035,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X3),X4)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1276]) ).

cnf(c_0_2036,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X3),X4)))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1277]) ).

cnf(c_0_2037,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X3),X4)))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1277]) ).

cnf(c_0_2038,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X5))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),top_top(fun(X1,bool))))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X4)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X5))) ),
    inference(split_conjunct,[status(thm)],[c_0_1283]) ).

cnf(c_0_2039,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,X2,X3)),hAPP(nat,X1,X2,X4)))
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,X2,esk91_4(X1,X3,X4,X2))),hAPP(nat,X1,X2,hAPP(nat,nat,suc,esk91_4(X1,X3,X4,X2)))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_1281]) ).

cnf(c_0_2040,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,X2,X3)),hAPP(nat,X1,X2,X4)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,X2,esk90_4(X1,X3,X4,X2))),hAPP(nat,X1,X2,hAPP(nat,nat,suc,esk90_4(X1,X3,X4,X2)))))
    | ~ order(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1284]) ).

cnf(c_0_2041,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,X2,X3)),hAPP(nat,X1,X2,X4)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,X2,esk89_4(X1,X3,X4,X2))),hAPP(nat,X1,X2,hAPP(nat,nat,suc,esk89_4(X1,X3,X4,X2)))))
    | ~ order(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1285]) ).

cnf(c_0_2042,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1243]) ).

cnf(c_0_2043,plain,
    ( X1 = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),hAPP(fun(nat,bool),nat,finite_card(nat),X1)))
    | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),X1),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),hAPP(fun(nat,bool),nat,finite_card(nat),X1))))) ),
    inference(split_conjunct,[status(thm)],[c_0_1286]) ).

cnf(c_0_2044,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X2)),hAPP(fun(X3,bool),nat,finite_card(X3),X4)))
    | ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X5),X2))
    | ~ hBOOL(hAPP(fun(fun(X1,X3),bool),bool,hAPP(fun(X1,X3),fun(fun(fun(X1,X3),bool),bool),member(fun(X1,X3)),X5),hAPP(fun(X1,fun(X3,bool)),fun(fun(X1,X3),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X3,bool)),fun(fun(X1,X3),bool)),pi(X1,X3),X2),hAPP(fun(X3,bool),fun(X1,fun(X3,bool)),combk(fun(X3,bool),X1),X4)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1287]) ).

cnf(c_0_2045,plain,
    ( ti(X1,X2) = ti(X1,X3)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(fun(X4,bool),fun(X1,bool),hAPP(fun(X4,X1),fun(fun(X4,bool),fun(X1,bool)),image(X4,X1),X5),X6)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X4,bool),fun(X1,bool),hAPP(fun(X4,X1),fun(fun(X4,bool),fun(X1,bool)),image(X4,X1),X5),X6)))
    | hAPP(X1,X4,hAPP(fun(X4,X1),fun(X1,X4),hAPP(fun(X4,bool),fun(fun(X4,X1),fun(X1,X4)),hilbert_inv_into(X4,X1),X6),X5),X2) != hAPP(X1,X4,hAPP(fun(X4,X1),fun(X1,X4),hAPP(fun(X4,bool),fun(fun(X4,X1),fun(X1,X4)),hilbert_inv_into(X4,X1),X6),X5),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1288]) ).

cnf(c_0_2046,plain,
    ( hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),member(product_prod(X1,X2)),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X5),X6)),X4))
    | ti(fun(product_prod(X1,X2),bool),X3) != ti(fun(product_prod(X1,X2),bool),X4)
    | ~ hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),member(product_prod(X1,X2)),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X5),X6)),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1256]) ).

cnf(c_0_2047,plain,
    ( hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),member(product_prod(X1,X2)),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X5),X6)),X3))
    | ti(fun(product_prod(X1,X2),bool),X3) != ti(fun(product_prod(X1,X2),bool),X4)
    | ~ hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),member(product_prod(X1,X2)),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X5),X6)),X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_1256]) ).

cnf(c_0_2048,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X2,X1,X3,X4)),X5))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X4),X6))
    | ~ hBOOL(hAPP(fun(fun(X2,X1),bool),bool,hAPP(fun(X2,X1),fun(fun(fun(X2,X1),bool),bool),member(fun(X2,X1)),X3),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,X1),bool),hAPP(fun(X2,bool),fun(fun(X2,fun(X1,bool)),fun(fun(X2,X1),bool)),pi(X2,X1),X6),hAPP(fun(X1,bool),fun(X2,fun(X1,bool)),combk(fun(X1,bool),X2),X5)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1289]) ).

cnf(c_0_2049,plain,
    ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(fun(X1,X2),bool),fun(fun(fun(X1,X2),bool),bool),ord_less_eq(fun(fun(X1,X2),bool)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X3),X4)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X5),X4)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X5),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1290]) ).

cnf(c_0_2050,plain,
    ( ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X2)),X1))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),X1))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X1),arrow_2064824852le_Lin)) ),
    inference(split_conjunct,[status(thm)],[c_0_1272]) ).

cnf(c_0_2051,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(split_conjunct,[status(thm)],[c_0_1243]) ).

cnf(c_0_2052,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(X1,bool)),combc(X1,fun(X1,bool),bool),member(X1)),X2)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(X1,bool)),combc(X1,fun(X1,bool),bool),member(X1)),X3)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1274]) ).

cnf(c_0_2053,plain,
    ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),esk12_1(X1)),esk13_1(X1))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,esk11_1(X1))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),esk12_1(X1)),esk13_1(X1))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,esk10_1(X1)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1247]) ).

cnf(c_0_2054,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,X1,X2)),X3)),hAPP(nat,nat,X1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3))))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk61_3(X2,X3,X1)),esk62_3(X2,X3,X1))) ),
    inference(split_conjunct,[status(thm)],[c_0_1279]) ).

cnf(c_0_2055,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1243]) ).

cnf(c_0_2056,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(split_conjunct,[status(thm)],[c_0_1245]) ).

cnf(c_0_2057,plain,
    ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X3),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X4),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),X5))))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk65_5(X2,X1,X3,X5,X4)),X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_1264]) ).

cnf(c_0_2058,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X2))
    | ~ linorder(X1)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5))) ),
    inference(split_conjunct,[status(thm)],[c_0_1291]) ).

cnf(c_0_2059,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
    | ~ linorder(X1)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5))) ),
    inference(split_conjunct,[status(thm)],[c_0_1291]) ).

cnf(c_0_2060,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X4))),hAPP(fun(X2,bool),nat,finite_card(X2),X4)))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_1292]) ).

cnf(c_0_2061,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X3),X4)))
    | ti(arrow_490897120le_alt,X1) != ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X2) != ti(arrow_490897120le_alt,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1276]) ).

cnf(c_0_2062,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X3),X4)))
    | ti(arrow_490897120le_alt,X1) != ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X1) != ti(arrow_490897120le_alt,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1277]) ).

cnf(c_0_2063,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X3),X4)))
    | ti(arrow_490897120le_alt,X1) != ti(arrow_490897120le_alt,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1276]) ).

cnf(c_0_2064,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X3),X4)))
    | ti(arrow_490897120le_alt,X2) != ti(arrow_490897120le_alt,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1277]) ).

cnf(c_0_2065,plain,
    ( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X2),X3) = ti(fun(X1,bool),X3)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X2),X3)),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1293]) ).

cnf(c_0_2066,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(split_conjunct,[status(thm)],[c_0_1245]) ).

cnf(c_0_2067,plain,
    ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X4)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X5)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),top_top(fun(X1,bool))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[c_0_1283]) ).

cnf(c_0_2068,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X2,X1,X3,X4)),hAPP(X2,fun(X1,bool),X5,X4)))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X4),X6))
    | ~ hBOOL(hAPP(fun(fun(X2,X1),bool),bool,hAPP(fun(X2,X1),fun(fun(fun(X2,X1),bool),bool),member(fun(X2,X1)),X3),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,X1),bool),hAPP(fun(X2,bool),fun(fun(X2,fun(X1,bool)),fun(fun(X2,X1),bool)),pi(X2,X1),X6),X5))) ),
    inference(split_conjunct,[status(thm)],[c_0_1294]) ).

cnf(c_0_2069,plain,
    ( hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),hAPP(X1,X4,X5,X2)),hAPP(X1,fun(X4,bool),X6,X2)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
    | ~ hBOOL(hAPP(fun(fun(X1,X4),bool),bool,hAPP(fun(X1,X4),fun(fun(fun(X1,X4),bool),bool),member(fun(X1,X4)),X5),hAPP(fun(X1,fun(X4,bool)),fun(fun(X1,X4),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X4,bool)),fun(fun(X1,X4),bool)),pi(X1,X4),X3),X6))) ),
    inference(split_conjunct,[status(thm)],[c_0_1295]) ).

cnf(c_0_2070,plain,
    ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),esk102_5(X1,X3,X2,X4,X5)),X5))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5))) ),
    inference(split_conjunct,[status(thm)],[c_0_1296]) ).

cnf(c_0_2071,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X4)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X5)))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less(fun(X2,bool)),X4),X5))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),inj_on(X2,X1),X3),X5)) ),
    inference(split_conjunct,[status(thm)],[c_0_1297]) ).

cnf(c_0_2072,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(bool,bool),fun(fun(X1,bool),fun(X1,bool)),combb(bool,bool,X1),fNot),X2)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1298]) ).

cnf(c_0_2073,plain,
    ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),esk101_5(X1,X3,X2,X4,X5)),X5))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5))) ),
    inference(split_conjunct,[status(thm)],[c_0_1299]) ).

cnf(c_0_2074,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(product_prod(X2,X1),bool),fun(X2,fun(X1,bool)),in_rel(X2,X1),X3),X4),X5))
    | ~ hBOOL(hAPP(fun(product_prod(X2,X1),bool),bool,hAPP(product_prod(X2,X1),fun(fun(product_prod(X2,X1),bool),bool),member(product_prod(X2,X1)),hAPP(X1,product_prod(X2,X1),hAPP(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),X4),X5)),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1300]) ).

cnf(c_0_2075,plain,
    ( hBOOL(hAPP(fun(fun(X1,bool),bool),bool,finite_finite_1(fun(X1,bool)),hAPP(fun(fun(X1,bool),bool),fun(fun(X1,bool),bool),collect(fun(X1,bool)),hAPP(fun(X1,bool),fun(fun(X1,bool),bool),hAPP(fun(fun(X1,bool),fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(fun(X1,bool),bool)),combc(fun(X1,bool),fun(X1,bool),bool),ord_less_eq(fun(X1,bool))),X2))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1301]) ).

cnf(c_0_2076,plain,
    ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X3),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X4),X5)))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk68_5(X2,X1,X3,X5,X4)),X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_1260]) ).

cnf(c_0_2077,plain,
    ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X3),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X4),X5)))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk33_5(X2,X1,X3,X5,X4)),X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_1261]) ).

cnf(c_0_2078,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,fun(X2,X3)),fun(fun(X1,bool),bool),inj_on(X1,fun(X2,X3)),hAPP(fun(X1,X3),fun(X1,fun(X2,X3)),hAPP(fun(X3,fun(X2,X3)),fun(fun(X1,X3),fun(X1,fun(X2,X3))),combb(X3,fun(X2,X3),X1),combk(X3,X2)),X4)),top_top(fun(X1,bool))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X4),top_top(fun(X1,bool)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1302]) ).

cnf(c_0_2079,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(split_conjunct,[status(thm)],[c_0_1243]) ).

cnf(c_0_2080,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(split_conjunct,[status(thm)],[c_0_1246]) ).

cnf(c_0_2081,plain,
    ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,X1))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),esk16_1(X1)),esk17_1(X1))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,esk15_1(X1)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1267]) ).

cnf(c_0_2082,plain,
    ( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X1),X2)),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X1),arrow_2064824852le_Lin)) ),
    inference(split_conjunct,[status(thm)],[c_0_1303]) ).

cnf(c_0_2083,plain,
    ( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X1),X2)),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X1),arrow_2064824852le_Lin)) ),
    inference(split_conjunct,[status(thm)],[c_0_1304]) ).

cnf(c_0_2084,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(split_conjunct,[status(thm)],[c_0_1245]) ).

cnf(c_0_2085,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ ordere236663937imp_le(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4))) ),
    inference(split_conjunct,[status(thm)],[c_0_1305]) ).

cnf(c_0_2086,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ ordere236663937imp_le(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3))) ),
    inference(split_conjunct,[status(thm)],[c_0_1306]) ).

cnf(c_0_2087,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)))
    | ~ ordere236663937imp_le(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1307]) ).

cnf(c_0_2088,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)))
    | ~ ordere236663937imp_le(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1308]) ).

cnf(c_0_2089,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ ordere236663937imp_le(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4))) ),
    inference(split_conjunct,[status(thm)],[c_0_1309]) ).

cnf(c_0_2090,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ ordere236663937imp_le(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3))) ),
    inference(split_conjunct,[status(thm)],[c_0_1310]) ).

cnf(c_0_2091,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)))
    | ~ ordere236663937imp_le(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1311]) ).

cnf(c_0_2092,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)))
    | ~ ordere236663937imp_le(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1312]) ).

cnf(c_0_2093,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X4)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X5)))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[c_0_1313]) ).

cnf(c_0_2094,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_1314]) ).

cnf(c_0_2095,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_1315]) ).

cnf(c_0_2096,plain,
    ( hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less_eq(fun(X1,X2)),X3),X4))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,esk39_4(X1,X2,X3,X4))),hAPP(X1,X2,X4,esk39_4(X1,X2,X3,X4))))
    | ~ ord(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1316]) ).

cnf(c_0_2097,plain,
    ( hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X4))
    | ~ ord(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X3,esk29_4(X2,X1,X3,X4))),hAPP(X2,X1,X4,esk29_4(X2,X1,X3,X4)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1317]) ).

cnf(c_0_2098,plain,
    ( hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),member(product_prod(X1,X2)),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X3),X4)),X5))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),hAPP(fun(product_prod(X1,X2),bool),fun(X1,fun(X2,bool)),in_rel(X1,X2),X5),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_1300]) ).

cnf(c_0_2099,plain,
    ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),combk(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),arrow_660593299e_indi),X1)),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X1),arrow_2064824852le_Lin)) ),
    inference(split_conjunct,[status(thm)],[c_0_1318]) ).

cnf(c_0_2100,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(split_conjunct,[status(thm)],[c_0_1245]) ).

cnf(c_0_2101,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk71_5(X2,X1,X3,X4,X5)),X5))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X4),X5))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X5)) ),
    inference(split_conjunct,[status(thm)],[c_0_1319]) ).

cnf(c_0_2102,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk71_5(X2,X1,X3,X4,X5)),X5))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X5))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[c_0_1319]) ).

cnf(c_0_2103,plain,
    ( hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X2) = hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X2,X3)
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X2),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,X1),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1320]) ).

cnf(c_0_2104,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X5)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | ~ ordere223160158up_add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1321]) ).

cnf(c_0_2105,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X5)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | ~ ordere779506340up_add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1322]) ).

cnf(c_0_2106,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X5)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | ~ ordere223160158up_add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1323]) ).

cnf(c_0_2107,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X5)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | ~ ordere223160158up_add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1324]) ).

cnf(c_0_2108,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X1,X2)),hAPP(nat,nat,X1,X3)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,X1,esk63_3(X2,X3,X1))),hAPP(nat,nat,X1,esk64_3(X2,X3,X1)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1325]) ).

cnf(c_0_2109,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X4)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X4))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1326]) ).

cnf(c_0_2110,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X4)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X4))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1327]) ).

cnf(c_0_2111,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(bool,bool),fun(fun(X1,bool),fun(X1,bool)),combb(bool,bool,X1),fNot),X2))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1298]) ).

cnf(c_0_2112,plain,
    ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab)),
    inference(split_conjunct,[status(thm)],[c_0_1328]) ).

cnf(c_0_2113,plain,
    ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba)),
    inference(split_conjunct,[status(thm)],[c_0_1329]) ).

cnf(c_0_2114,plain,
    ( hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),hAPP(fun(X1,X2),fun(X2,X1),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)),hilbert_inv_into(X1,X2),top_top(fun(X1,bool))),X3)),X4)) = ti(fun(X2,bool),X4)
    | hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),top_top(fun(X1,bool))) != top_top(fun(X2,bool)) ),
    inference(split_conjunct,[status(thm)],[c_0_1330]) ).

cnf(c_0_2115,plain,
    ( hAPP(X1,X2,X3,hAPP(X2,X1,hAPP(fun(X1,X2),fun(X2,X1),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)),hilbert_inv_into(X1,X2),X4),X3),X5)) = ti(X2,X5)
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X5),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X4))) ),
    inference(split_conjunct,[status(thm)],[c_0_1331]) ).

cnf(c_0_2116,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(split_conjunct,[status(thm)],[c_0_1246]) ).

cnf(c_0_2117,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X3),X4)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X2) != ti(arrow_490897120le_alt,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1276]) ).

cnf(c_0_2118,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X3),X4)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X2) != ti(arrow_490897120le_alt,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1276]) ).

cnf(c_0_2119,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X3),X4)))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) != ti(arrow_490897120le_alt,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1277]) ).

cnf(c_0_2120,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X3),X4)))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X1) != ti(arrow_490897120le_alt,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1277]) ).

cnf(c_0_2121,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
    | ~ linordered_idom(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)),zero_zero(X1))) ),
    inference(split_conjunct,[status(thm)],[c_0_1332]) ).

cnf(c_0_2122,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
    | ~ linord219039673up_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)),zero_zero(X1))) ),
    inference(split_conjunct,[status(thm)],[c_0_1333]) ).

cnf(c_0_2123,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1)))
    | ~ linord219039673up_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)),zero_zero(X1))) ),
    inference(split_conjunct,[status(thm)],[c_0_1334]) ).

cnf(c_0_2124,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),ring_1_Ints(X1)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),ring_1_Ints(X1)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),ring_1_Ints(X1)))
    | ~ ring_1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1335]) ).

cnf(c_0_2125,plain,
    ( ti(fun(X1,bool),X2) = hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),esk102_5(X1,X3,X2,X4,X5))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5))) ),
    inference(split_conjunct,[status(thm)],[c_0_1296]) ).

cnf(c_0_2126,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X2)),hAPP(fun(X1,bool),nat,finite_card(X1),X3)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1336]) ).

cnf(c_0_2127,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X3)),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1337]) ).

cnf(c_0_2128,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1338]) ).

cnf(c_0_2129,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X3)),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1339]) ).

cnf(c_0_2130,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1340]) ).

cnf(c_0_2131,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1340]) ).

cnf(c_0_2132,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)))
    | ~ ordere236663937imp_le(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_1305]) ).

cnf(c_0_2133,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)))
    | ~ ordere236663937imp_le(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_1306]) ).

cnf(c_0_2134,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | ~ ordere223160158up_add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1341]) ).

cnf(c_0_2135,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
    | ~ ordere223160158up_add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1342]) ).

cnf(c_0_2136,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)))
    | ~ ordere236663937imp_le(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_1309]) ).

cnf(c_0_2137,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)))
    | ~ ordere236663937imp_le(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_1310]) ).

cnf(c_0_2138,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | ~ ordere779506340up_add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1343]) ).

cnf(c_0_2139,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
    | ~ ordere779506340up_add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1344]) ).

cnf(c_0_2140,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X4),X5))
    | hAPP(X1,X2,X3,esk71_5(X2,X1,X3,X4,X5)) != hAPP(X1,X2,X4,esk71_5(X2,X1,X3,X4,X5))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X5)) ),
    inference(split_conjunct,[status(thm)],[c_0_1319]) ).

cnf(c_0_2141,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X5))
    | hAPP(X1,X2,X3,esk71_5(X2,X1,X3,X4,X5)) != hAPP(X1,X2,X4,esk71_5(X2,X1,X3,X4,X5))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[c_0_1319]) ).

cnf(c_0_2142,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1345]) ).

cnf(c_0_2143,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X3)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1314]) ).

cnf(c_0_2144,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1346]) ).

cnf(c_0_2145,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X3)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1315]) ).

cnf(c_0_2146,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X2),X3)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1347]) ).

cnf(c_0_2147,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),zero_zero(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),zero_zero(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
    | ~ ordere216010020id_add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1348]) ).

cnf(c_0_2148,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),zero_zero(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),zero_zero(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1)))
    | ~ ordere216010020id_add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1349]) ).

cnf(c_0_2149,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),zero_zero(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),zero_zero(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
    | ~ ordere216010020id_add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1350]) ).

cnf(c_0_2150,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),zero_zero(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),zero_zero(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1)))
    | ~ ordere216010020id_add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1351]) ).

cnf(c_0_2151,plain,
    ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,X1))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),esk16_1(X1)),esk17_1(X1))),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),esk15_1(X1),X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_1267]) ).

cnf(c_0_2152,plain,
    ( ti(X1,X2) = hAPP(X3,X1,X4,esk101_5(X1,X3,X2,X4,X5))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5))) ),
    inference(split_conjunct,[status(thm)],[c_0_1299]) ).

cnf(c_0_2153,plain,
    hBOOL(hAPP(fun(fun(X1,X1),bool),bool,hAPP(fun(X1,X1),fun(fun(fun(X1,X1),bool),bool),member(fun(X1,X1)),combi(X1)),hAPP(fun(X1,fun(X1,bool)),fun(fun(X1,X1),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X1,bool)),fun(fun(X1,X1),bool)),pi(X1,X1),X2),hAPP(fun(X1,bool),fun(X1,fun(X1,bool)),combk(fun(X1,bool),X1),X2)))),
    inference(split_conjunct,[status(thm)],[c_0_1352]) ).

cnf(c_0_2154,plain,
    ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),X2)),
    inference(split_conjunct,[status(thm)],[c_0_1353]) ).

cnf(c_0_2155,plain,
    ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),X1)),
    inference(split_conjunct,[status(thm)],[c_0_1354]) ).

cnf(c_0_2156,plain,
    ( hAPP(fun(X1,bool),nat,finite_card(X1),X2) = hAPP(fun(X1,bool),nat,hAPP(nat,fun(fun(X1,bool),nat),hAPP(fun(X1,nat),fun(nat,fun(fun(X1,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(X1,nat),fun(nat,fun(fun(X1,bool),nat))),finite_fold_image(nat,X1),plus_plus(nat)),hAPP(nat,fun(X1,nat),combk(nat,X1),one_one(nat))),zero_zero(nat)),X2)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1355]) ).

cnf(c_0_2157,plain,
    ( hAPP(fun(X1,bool),nat,finite_card(X1),X2) = hAPP(fun(X1,bool),nat,hAPP(nat,fun(fun(X1,bool),nat),hAPP(fun(X1,nat),fun(nat,fun(fun(X1,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(X1,nat),fun(nat,fun(fun(X1,bool),nat))),finite_fold_image(nat,X1),plus_plus(nat)),hAPP(nat,fun(X1,nat),combk(nat,X1),one_one(nat))),zero_zero(nat)),X2)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1356]) ).

cnf(c_0_2158,plain,
    ( ti(fun(X1,bool),X2) = ti(fun(X1,bool),X3)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X3)),hAPP(fun(X1,bool),nat,finite_card(X1),X2)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1357]) ).

cnf(c_0_2159,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5)))
    | ti(fun(X1,bool),X2) != hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X6)
    | ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X6),X5)) ),
    inference(split_conjunct,[status(thm)],[c_0_1296]) ).

cnf(c_0_2160,plain,
    hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,nat),fun(fun(nat,bool),bool),inj_on(nat,nat),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),X1)),X2)),
    inference(split_conjunct,[status(thm)],[c_0_1358]) ).

cnf(c_0_2161,plain,
    hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),X1)))),
    inference(split_conjunct,[status(thm)],[c_0_1359]) ).

cnf(c_0_2162,plain,
    hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X1)))),
    inference(split_conjunct,[status(thm)],[c_0_1360]) ).

cnf(c_0_2163,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X5)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X5))
    | ~ comm_semiring_1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1361]) ).

cnf(c_0_2164,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X2,X1,X3,X4)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X5)))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X4),X5)) ),
    inference(split_conjunct,[status(thm)],[c_0_1362]) ).

cnf(c_0_2165,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)),zero_zero(X1)))
    | ~ linordered_idom(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1))) ),
    inference(split_conjunct,[status(thm)],[c_0_1332]) ).

cnf(c_0_2166,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)),zero_zero(X1)))
    | ~ linord219039673up_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1))) ),
    inference(split_conjunct,[status(thm)],[c_0_1333]) ).

cnf(c_0_2167,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)),zero_zero(X1)))
    | ~ linord219039673up_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1))) ),
    inference(split_conjunct,[status(thm)],[c_0_1334]) ).

cnf(c_0_2168,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X1))) ),
    inference(split_conjunct,[status(thm)],[c_0_1363]) ).

cnf(c_0_2169,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ hBOOL(hAPP(fun(sum_sum(X3,X1),bool),bool,finite_finite_1(sum_sum(X3,X1)),hAPP(fun(X1,bool),fun(sum_sum(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X1,bool),fun(sum_sum(X3,X1),bool)),sum_Plus(X3,X1),X4),X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_1364]) ).

cnf(c_0_2170,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ hBOOL(hAPP(fun(sum_sum(X1,X3),bool),bool,finite_finite_1(sum_sum(X1,X3)),hAPP(fun(X3,bool),fun(sum_sum(X1,X3),bool),hAPP(fun(X1,bool),fun(fun(X3,bool),fun(sum_sum(X1,X3),bool)),sum_Plus(X1,X3),X2),X4))) ),
    inference(split_conjunct,[status(thm)],[c_0_1365]) ).

cnf(c_0_2171,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3))
    | ~ hBOOL(hAPP(fun(sum_sum(X1,X2),bool),bool,finite_finite_1(sum_sum(X1,X2)),hAPP(fun(X2,bool),fun(sum_sum(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X2,bool),fun(sum_sum(X1,X2),bool)),sum_Plus(X1,X2),X3),X4))) ),
    inference(split_conjunct,[status(thm)],[c_0_1366]) ).

cnf(c_0_2172,plain,
    ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
    | ~ hBOOL(hAPP(fun(sum_sum(X1,X2),bool),bool,finite_finite_1(sum_sum(X1,X2)),hAPP(fun(X2,bool),fun(sum_sum(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X2,bool),fun(sum_sum(X1,X2),bool)),sum_Plus(X1,X2),X3),X4))) ),
    inference(split_conjunct,[status(thm)],[c_0_1366]) ).

cnf(c_0_2173,plain,
    ( hBOOL(hAPP(fun(X1,fun(X2,bool)),bool,hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,fun(X2,bool)),bool),ord_less_eq(fun(X1,fun(X2,bool))),X3),X4))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X4,esk50_4(X2,X1,X4,X3)),esk51_4(X2,X1,X4,X3))) ),
    inference(split_conjunct,[status(thm)],[c_0_1367]) ).

cnf(c_0_2174,plain,
    ( hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,X1),X2))
    | hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),esk32_2(X1,X2)),arrow_1111136790e_Prof)) ),
    inference(split_conjunct,[status(thm)],[c_0_1320]) ).

cnf(c_0_2175,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
    | ~ ordere216010020id_add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1368]) ).

cnf(c_0_2176,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
    | ~ ordere216010020id_add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1369]) ).

cnf(c_0_2177,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
    | ~ ordere216010020id_add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1370]) ).

cnf(c_0_2178,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
    | ~ ordere216010020id_add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1371]) ).

cnf(c_0_2179,plain,
    hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),combb(X3,X2,X1),X4),X5)),top_top(fun(X1,bool))) = hAPP(fun(X3,bool),fun(X2,bool),hAPP(fun(X3,X2),fun(fun(X3,bool),fun(X2,bool)),image(X3,X2),X4),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X5),top_top(fun(X1,bool)))),
    inference(split_conjunct,[status(thm)],[c_0_1372]) ).

cnf(c_0_2180,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),esk26_2(X1,X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_1373]) ).

cnf(c_0_2181,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
    | ~ ordere216010020id_add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1374]) ).

cnf(c_0_2182,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
    | ~ ordere216010020id_add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1375]) ).

cnf(c_0_2183,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
    | ~ linordered_semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1376]) ).

cnf(c_0_2184,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
    | ~ ordere216010020id_add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1377]) ).

cnf(c_0_2185,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X4))
    | ~ ordere216010020id_add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1378]) ).

cnf(c_0_2186,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ linordered_field(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),esk99_3(X1,X2,X3)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1379]) ).

cnf(c_0_2187,plain,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),esk19_0)),
    inference(split_conjunct,[status(thm)],[c_0_1380]) ).

cnf(c_0_2188,plain,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),esk18_0)),
    inference(split_conjunct,[status(thm)],[c_0_1381]) ).

cnf(c_0_2189,plain,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba)),
    inference(split_conjunct,[status(thm)],[c_0_1382]) ).

cnf(c_0_2190,plain,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab)),
    inference(split_conjunct,[status(thm)],[c_0_1383]) ).

cnf(c_0_2191,plain,
    hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),hAPP(fun(X4,bool),fun(X1,bool),hAPP(fun(X4,X1),fun(fun(X4,bool),fun(X1,bool)),image(X4,X1),X5),X6)) = hAPP(fun(X4,bool),fun(X2,bool),hAPP(fun(X4,X2),fun(fun(X4,bool),fun(X2,bool)),image(X4,X2),hAPP(fun(X4,X1),fun(X4,X2),hAPP(fun(X1,X2),fun(fun(X4,X1),fun(X4,X2)),combb(X1,X2,X4),X3),X5)),X6),
    inference(split_conjunct,[status(thm)],[c_0_1384]) ).

cnf(c_0_2192,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
    | ~ dense_linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),esk38_4(X1,X4,X2,X3)),X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_1385]) ).

cnf(c_0_2193,plain,
    ( ti(X1,X2) = ti(X1,X3)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
    | hAPP(X1,X5,X6,X2) != hAPP(X1,X5,X6,X3)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X5),fun(fun(X1,bool),bool),inj_on(X1,X5),X6),X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_1386]) ).

cnf(c_0_2194,plain,
    ( ti(X1,X5) = ti(X1,X6)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X4))
    | hAPP(X1,X2,X3,X5) != hAPP(X1,X2,X3,X6) ),
    inference(split_conjunct,[status(thm)],[c_0_1387]) ).

cnf(c_0_2195,plain,
    ( ti(X1,X4) = ti(X1,X5)
    | hAPP(X1,X2,X3,X4) != hAPP(X1,X2,X3,X5)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X6))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X6))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X6)) ),
    inference(split_conjunct,[status(thm)],[c_0_1388]) ).

cnf(c_0_2196,plain,
    ( ti(X1,X2) = ti(X1,X3)
    | hAPP(X1,X4,X5,X2) != hAPP(X1,X4,X5,X3)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X6))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X6))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X4),fun(fun(X1,bool),bool),inj_on(X1,X4),X5),X6)) ),
    inference(split_conjunct,[status(thm)],[c_0_1389]) ).

cnf(c_0_2197,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5)))
    | ti(X1,X2) != hAPP(X3,X1,X4,X6)
    | ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X5)) ),
    inference(split_conjunct,[status(thm)],[c_0_1299]) ).

cnf(c_0_2198,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5)))
    | ti(X1,X2) != hAPP(X3,X1,X4,X6)
    | ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X5)) ),
    inference(split_conjunct,[status(thm)],[c_0_1390]) ).

cnf(c_0_2199,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5)))
    | ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X5))
    | ti(X1,X2) != hAPP(X3,X1,X4,X6) ),
    inference(split_conjunct,[status(thm)],[c_0_1391]) ).

cnf(c_0_2200,plain,
    ( hBOOL(hAPP(product_prod(X1,X2),bool,X3,X4))
    | ~ hBOOL(hAPP(product_prod(X1,X2),bool,X3,hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),esk7_3(X1,X2,X3)),esk8_3(X1,X2,X3)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1392]) ).

cnf(c_0_2201,plain,
    ( hAPP(X1,X2,X3,X5) = hAPP(X1,X2,X3,X6)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X4))
    | ti(X1,X5) != ti(X1,X6) ),
    inference(split_conjunct,[status(thm)],[c_0_1387]) ).

cnf(c_0_2202,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
    | ~ linord219039673up_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_1393]) ).

cnf(c_0_2203,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
    | ~ linord219039673up_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_1394]) ).

cnf(c_0_2204,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X1,X2)),hAPP(nat,nat,X1,X3)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk63_3(X2,X3,X1)),esk64_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1325]) ).

cnf(c_0_2205,plain,
    ( hAPP(X1,X2,hAPP(fun(X2,X1),fun(X1,X2),hAPP(fun(X2,bool),fun(fun(X2,X1),fun(X1,X2)),hilbert_inv_into(X2,X1),X3),X4),hAPP(X2,X1,X4,X5)) = ti(X2,X5)
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X5),X3))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),inj_on(X2,X1),X4),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1395]) ).

cnf(c_0_2206,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X3,X4),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X6,X4),X5))
    | ~ hBOOL(hAPP(fun(X2,fun(X1,bool)),bool,hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),bool),ord_less_eq(fun(X2,fun(X1,bool))),X6),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1396]) ).

cnf(c_0_2207,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X3,X4),X5))
    | ~ hBOOL(hAPP(fun(X2,fun(X1,bool)),bool,hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),bool),ord_less_eq(fun(X2,fun(X1,bool))),X6),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X6,X4),X5)) ),
    inference(split_conjunct,[status(thm)],[c_0_1397]) ).

cnf(c_0_2208,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X2)),hAPP(fun(X1,bool),nat,finite_card(X1),X3)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1398]) ).

cnf(c_0_2209,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X2)),hAPP(fun(X1,bool),nat,finite_card(X1),X3)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1399]) ).

cnf(c_0_2210,plain,
    ( hAPP(X1,X2,hAPP(fun(X2,X1),fun(X1,X2),hAPP(fun(X2,bool),fun(fun(X2,X1),fun(X1,X2)),hilbert_inv_into(X2,X1),X3),X4),X5) = ti(X2,X6)
    | hAPP(X2,X1,X4,X6) != ti(X1,X5)
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X6),X3))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),inj_on(X2,X1),X4),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1400]) ).

cnf(c_0_2211,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1401]) ).

cnf(c_0_2212,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)))),
    inference(split_conjunct,[status(thm)],[c_0_1402]) ).

cnf(c_0_2213,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X1)))),
    inference(split_conjunct,[status(thm)],[c_0_1403]) ).

cnf(c_0_2214,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X4),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_1404]) ).

cnf(c_0_2215,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_1405]) ).

cnf(c_0_2216,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X4),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_1406]) ).

cnf(c_0_2217,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_1407]) ).

cnf(c_0_2218,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),hAPP(nat,nat,suc,X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_1408]) ).

cnf(c_0_2219,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),hAPP(nat,nat,suc,X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_1409]) ).

cnf(c_0_2220,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),hAPP(nat,nat,suc,X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_1410]) ).

cnf(c_0_2221,plain,
    hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X2,X1,X3,X4)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),top_top(fun(X2,bool))))),
    inference(split_conjunct,[status(thm)],[c_0_1411]) ).

cnf(c_0_2222,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X5))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X5)) ),
    inference(split_conjunct,[status(thm)],[c_0_1412]) ).

cnf(c_0_2223,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1413]) ).

cnf(c_0_2224,plain,
    ( hAPP(fun(X1,X2),fun(X2,X1),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)),hilbert_inv_into(X1,X2),top_top(fun(X1,bool))),X3) = ti(fun(X2,X1),X4)
    | hAPP(X1,X2,X3,hAPP(X2,X1,X4,esk34_4(X1,X2,X4,X3))) != ti(X2,esk34_4(X1,X2,X4,X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),top_top(fun(X1,bool)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1414]) ).

cnf(c_0_2225,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)),X3)
    | ~ comm_semiring_1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1415]) ).

cnf(c_0_2226,plain,
    ( hBOOL(hAPP(fun(sum_sum(X1,X2),bool),bool,finite_finite_1(sum_sum(X1,X2)),hAPP(fun(X2,bool),fun(sum_sum(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X2,bool),fun(sum_sum(X1,X2),bool)),sum_Plus(X1,X2),X3),X4)))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1416]) ).

cnf(c_0_2227,plain,
    ( hBOOL(hAPP(fun(sum_sum(X1,X2),bool),bool,finite_finite_1(sum_sum(X1,X2)),hAPP(fun(X2,bool),fun(sum_sum(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X2,bool),fun(sum_sum(X1,X2),bool)),sum_Plus(X1,X2),X3),X4)))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1366]) ).

cnf(c_0_2228,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X4),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1417]) ).

cnf(c_0_2229,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1418]) ).

cnf(c_0_2230,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_1419]) ).

cnf(c_0_2231,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1420]) ).

cnf(c_0_2232,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1421]) ).

cnf(c_0_2233,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_1401]) ).

cnf(c_0_2234,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1401]) ).

cnf(c_0_2235,plain,
    ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,X1))
    | hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),esk15_1(X1)),arrow_1111136790e_Prof)) ),
    inference(split_conjunct,[status(thm)],[c_0_1267]) ).

cnf(c_0_2236,plain,
    ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1))
    | hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),esk10_1(X1)),arrow_1111136790e_Prof)) ),
    inference(split_conjunct,[status(thm)],[c_0_1247]) ).

cnf(c_0_2237,plain,
    ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1))
    | hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),esk11_1(X1)),arrow_1111136790e_Prof)) ),
    inference(split_conjunct,[status(thm)],[c_0_1247]) ).

cnf(c_0_2238,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X3,X4)),hAPP(X2,X1,X5,X4)))
    | ~ ord(X1)
    | ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X5)) ),
    inference(split_conjunct,[status(thm)],[c_0_1317]) ).

cnf(c_0_2239,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X3,X4)),hAPP(X2,X1,X5,X4)))
    | ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X5))
    | ~ ord(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1422]) ).

cnf(c_0_2240,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X3,X4)),hAPP(X2,X1,X5,X4)))
    | ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X5))
    | ~ ord(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1423]) ).

cnf(c_0_2241,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X2)),X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_1424]) ).

cnf(c_0_2242,plain,
    ( ti(X1,X2) = ti(X1,X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),X2))
    | hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X5),X2) != hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X3)
    | ~ linorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1425]) ).

cnf(c_0_2243,plain,
    ( ti(X1,X2) = ti(X1,X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X5))
    | hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X5) != hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X3),X4)
    | ~ linorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1426]) ).

cnf(c_0_2244,plain,
    ( ti(X1,X2) = ti(X1,X4)
    | ~ linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X5))
    | hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X3) != hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5) ),
    inference(split_conjunct,[status(thm)],[c_0_1427]) ).

cnf(c_0_2245,plain,
    ( ti(X1,X3) = ti(X1,X5)
    | ~ linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X5))
    | hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X3) != hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5) ),
    inference(split_conjunct,[status(thm)],[c_0_1427]) ).

cnf(c_0_2246,plain,
    ( hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less(fun(X2,X1)),X3),X4))
    | hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X4),X3))
    | ~ ord(X1)
    | ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_1428]) ).

cnf(c_0_2247,plain,
    ( hBOOL(hAPP(fun(X1,fun(X2,bool)),bool,hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,fun(X2,bool)),bool),ord_less_eq(fun(X1,fun(X2,bool))),X3),X4))
    | hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X3,esk50_4(X2,X1,X4,X3)),esk51_4(X2,X1,X4,X3))) ),
    inference(split_conjunct,[status(thm)],[c_0_1367]) ).

cnf(c_0_2248,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),esk38_4(X1,X4,X2,X3)),X3))
    | ~ dense_linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1385]) ).

cnf(c_0_2249,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)))
    | ~ linord219039673up_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1393]) ).

cnf(c_0_2250,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)))
    | ~ linord219039673up_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1394]) ).

cnf(c_0_2251,plain,
    ( hAPP(fun(sum_sum(X1,X2),bool),nat,finite_card(sum_sum(X1,X2)),hAPP(fun(X2,bool),fun(sum_sum(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X2,bool),fun(sum_sum(X1,X2),bool)),sum_Plus(X1,X2),X3),X4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X3)),hAPP(fun(X2,bool),nat,finite_card(X2),X4))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1429]) ).

cnf(c_0_2252,plain,
    ( hAPP(fun(sum_sum(X1,X2),bool),nat,finite_card(sum_sum(X1,X2)),hAPP(fun(X2,bool),fun(sum_sum(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X2,bool),fun(sum_sum(X1,X2),bool)),sum_Plus(X1,X2),X3),X4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X3)),hAPP(fun(X2,bool),nat,finite_card(X2),X4))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1430]) ).

cnf(c_0_2253,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X4),X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | hAPP(fun(X3,bool),nat,finite_card(X3),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X4),X2)) != hAPP(fun(X1,bool),nat,finite_card(X1),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1431]) ).

cnf(c_0_2254,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | hAPP(fun(X2,bool),nat,finite_card(X2),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X4)) != hAPP(fun(X1,bool),nat,finite_card(X1),X4)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_1432]) ).

cnf(c_0_2255,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_1363]) ).

cnf(c_0_2256,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1363]) ).

cnf(c_0_2257,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1433]) ).

cnf(c_0_2258,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1434]) ).

cnf(c_0_2259,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1435]) ).

cnf(c_0_2260,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1436]) ).

cnf(c_0_2261,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1437]) ).

cnf(c_0_2262,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1438]) ).

cnf(c_0_2263,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1439]) ).

cnf(c_0_2264,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1440]) ).

cnf(c_0_2265,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_1401]) ).

cnf(c_0_2266,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),esk94_2(X1,X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1441]) ).

cnf(c_0_2267,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1442]) ).

cnf(c_0_2268,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1443]) ).

cnf(c_0_2269,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1444]) ).

cnf(c_0_2270,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1445]) ).

cnf(c_0_2271,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1446]) ).

cnf(c_0_2272,plain,
    ( hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X3) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5)
    | ~ linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X5))
    | ti(X1,X3) != ti(X1,X5)
    | ti(X1,X2) != ti(X1,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1427]) ).

cnf(c_0_2273,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),top_top(fun(X3,bool)))))
    | ti(X1,X2) != hAPP(X3,X1,X4,X5) ),
    inference(split_conjunct,[status(thm)],[c_0_1447]) ).

cnf(c_0_2274,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),hAPP(nat,nat,suc,X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1409]) ).

cnf(c_0_2275,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),hAPP(nat,nat,suc,X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1410]) ).

cnf(c_0_2276,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),hAPP(nat,nat,suc,X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1448]) ).

cnf(c_0_2277,plain,
    ( hAPP(fun(X3,bool),nat,finite_card(X3),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X4),X2)) = hAPP(fun(X1,bool),nat,finite_card(X1),X2)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X4),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1431]) ).

cnf(c_0_2278,plain,
    ( ~ ord(X1)
    | ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less(fun(X2,X1)),X3),X4))
    | ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X4),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1428]) ).

cnf(c_0_2279,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),esk38_4(X1,X4,X2,X3)))
    | ~ dense_linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1385]) ).

cnf(c_0_2280,plain,
    ( ti(fun(X1,bool),X2) = ti(fun(X1,bool),X3)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1449]) ).

cnf(c_0_2281,plain,
    ( ti(fun(X1,bool),X2) = ti(fun(X1,bool),X3)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1450]) ).

cnf(c_0_2282,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
    | ~ order(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1451]) ).

cnf(c_0_2283,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | ~ preorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1452]) ).

cnf(c_0_2284,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
    | ~ order(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1453]) ).

cnf(c_0_2285,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | ~ preorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1454]) ).

cnf(c_0_2286,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | ~ preorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1455]) ).

cnf(c_0_2287,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
    | ~ order(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1456]) ).

cnf(c_0_2288,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | ~ preorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1457]) ).

cnf(c_0_2289,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
    | ~ order(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1458]) ).

cnf(c_0_2290,plain,
    ( hAPP(X1,X2,hAPP(fun(X2,X1),fun(X1,X2),hAPP(fun(X2,bool),fun(fun(X2,X1),fun(X1,X2)),hilbert_inv_into(X2,X1),top_top(fun(X2,bool))),X3),hAPP(X2,X1,X3,X4)) = ti(X2,X4)
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),inj_on(X2,X1),X3),top_top(fun(X2,bool)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1459]) ).

cnf(c_0_2291,plain,
    hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),p),arrow_1111136790e_Prof)),
    inference(split_conjunct,[status(thm)],[c_0_1460]) ).

cnf(c_0_2292,plain,
    ( hAPP(X1,X2,hAPP(fun(X2,X1),fun(X1,X2),hAPP(fun(X2,bool),fun(fun(X2,X1),fun(X1,X2)),hilbert_inv_into(X2,X1),top_top(fun(X2,bool))),X3),X4) = ti(X2,X5)
    | hAPP(X2,X1,X3,X5) != ti(X1,X4)
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),inj_on(X2,X1),X3),top_top(fun(X2,bool)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1461]) ).

cnf(c_0_2293,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1462]) ).

cnf(c_0_2294,plain,
    arrow_1111136790e_Prof = hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(arrow_660593299e_indi,bool),fun(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),top_top(fun(arrow_660593299e_indi,bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),arrow_660593299e_indi),arrow_2064824852le_Lin)),
    inference(split_conjunct,[status(thm)],[c_0_1463]) ).

cnf(c_0_2295,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X3) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4),X2)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1464]) ).

cnf(c_0_2296,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4))
    | ~ comm_semiring_1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1465]) ).

cnf(c_0_2297,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),X4)
    | ~ comm_semiring_1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1466]) ).

cnf(c_0_2298,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4))
    | ~ ab_semigroup_add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1467]) ).

cnf(c_0_2299,plain,
    ( X2 = X1
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),hAPP(nat,nat,suc,X1))) ),
    inference(split_conjunct,[status(thm)],[c_0_1468]) ).

cnf(c_0_2300,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),hAPP(nat,nat,suc,X1))) ),
    inference(split_conjunct,[status(thm)],[c_0_1469]) ).

cnf(c_0_2301,plain,
    ( X3 = X2
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1401]) ).

cnf(c_0_2302,plain,
    ( ti(X1,X2) = zero_zero(X1)
    | ~ ordere216010020id_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) != zero_zero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1470]) ).

cnf(c_0_2303,plain,
    ( ti(X1,X3) = zero_zero(X1)
    | ~ ordere216010020id_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) != zero_zero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1470]) ).

cnf(c_0_2304,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),X3) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3)),
    inference(split_conjunct,[status(thm)],[c_0_1471]) ).

cnf(c_0_2305,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),X2))
    | hAPP(nat,nat,suc,X1) = X2
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1472]) ).

cnf(c_0_2306,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) = zero_zero(X1)
    | ~ ordere216010020id_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
    | ti(X1,X3) != zero_zero(X1)
    | ti(X1,X2) != zero_zero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1470]) ).

cnf(c_0_2307,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1442]) ).

cnf(c_0_2308,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1443]) ).

cnf(c_0_2309,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1473]) ).

cnf(c_0_2310,plain,
    hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),X1))) = hAPP(nat,nat,suc,X1),
    inference(split_conjunct,[status(thm)],[c_0_1474]) ).

cnf(c_0_2311,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X4)))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_1475]) ).

cnf(c_0_2312,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk69_4(X2,X1,X3,X4)),X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_1476]) ).

cnf(c_0_2313,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk70_4(X2,X1,X3,X4)),X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_1476]) ).

cnf(c_0_2314,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk30_4(X1,X2,X3,X4)),X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_1389]) ).

cnf(c_0_2315,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk31_4(X1,X2,X3,X4)),X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_1389]) ).

cnf(c_0_2316,plain,
    ( X1 = hAPP(nat,nat,suc,X2)
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,suc,X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_1477]) ).

cnf(c_0_2317,plain,
    ( X1 = hAPP(nat,nat,suc,X2)
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,suc,X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_1478]) ).

cnf(c_0_2318,plain,
    ( X2 = hAPP(nat,nat,suc,esk94_2(X1,X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1441]) ).

cnf(c_0_2319,plain,
    ( X1 = hAPP(nat,nat,suc,esk92_2(X2,X1))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X2)),X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_1479]) ).

cnf(c_0_2320,plain,
    ( hBOOL(hAPP(nat,bool,X3,X1))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk86_3(X3,X1,X2)),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,X3,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1480]) ).

cnf(c_0_2321,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ preorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1481]) ).

cnf(c_0_2322,plain,
    hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X1))) = X1,
    inference(split_conjunct,[status(thm)],[c_0_1482]) ).

cnf(c_0_2323,plain,
    ( X1 = zero_zero(nat)
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk85_2(X1,X2)),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_1483]) ).

cnf(c_0_2324,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk53_3(X1,X3,X2)),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1484]) ).

cnf(c_0_2325,plain,
    ( hBOOL(hAPP(product_prod(X1,X2),bool,X3,hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X4),X5)))
    | ~ hBOOL(hAPP(product_prod(X1,X2),bool,X3,esk6_3(X1,X2,X3))) ),
    inference(split_conjunct,[status(thm)],[c_0_1392]) ).

cnf(c_0_2326,plain,
    ( hBOOL(hAPP(nat,bool,X3,X1))
    | hBOOL(hAPP(nat,bool,X3,hAPP(nat,nat,suc,esk86_3(X3,X1,X2))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,X3,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1480]) ).

cnf(c_0_2327,plain,
    ( hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X4))
    | ~ ord(X1)
    | ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less(fun(X2,X1)),X3),X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_1428]) ).

cnf(c_0_2328,plain,
    ( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X2),top_top(fun(X1,bool))) = top_top(fun(X1,bool))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X2),top_top(fun(X1,bool))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1485]) ).

cnf(c_0_2329,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | X1 = X2
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_1401]) ).

cnf(c_0_2330,plain,
    ( X3 = X2
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1401]) ).

cnf(c_0_2331,plain,
    ( X1 = X2
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_1486]) ).

cnf(c_0_2332,plain,
    ( X1 = X2
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),hAPP(nat,nat,suc,X1))) ),
    inference(split_conjunct,[status(thm)],[c_0_1487]) ).

cnf(c_0_2333,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | X1 = X2
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_1488]) ).

cnf(c_0_2334,plain,
    ( X1 = X2
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_1489]) ).

cnf(c_0_2335,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_1490]) ).

cnf(c_0_2336,plain,
    ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),X1)),
    inference(split_conjunct,[status(thm)],[c_0_1491]) ).

cnf(c_0_2337,plain,
    ( ti(fun(X1,bool),X2) = ti(fun(X1,bool),X3)
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1492]) ).

cnf(c_0_2338,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3))
    | ti(fun(X1,bool),X2) = ti(fun(X1,bool),X3)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1493]) ).

cnf(c_0_2339,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1494]) ).

cnf(c_0_2340,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1492]) ).

cnf(c_0_2341,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1493]) ).

cnf(c_0_2342,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X2))
    | X1 != hAPP(nat,nat,suc,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1483]) ).

cnf(c_0_2343,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),esk75_1(X2)))
    | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X1),X2))
    | ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1495]) ).

cnf(c_0_2344,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),esk73_1(X2)))
    | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X1),X2))
    | ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1496]) ).

cnf(c_0_2345,plain,
    ( hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
    | hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),esk79_2(X2,X1)),one_one(nat))))
    | ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1497]) ).

cnf(c_0_2346,plain,
    ( ~ linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X2) != ti(X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1498]) ).

cnf(c_0_2347,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_1424]) ).

cnf(c_0_2348,plain,
    ( ti(X1,X2) = ti(X1,X3)
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1499]) ).

cnf(c_0_2349,plain,
    ( ti(X1,X3) = ti(X1,X2)
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1500]) ).

cnf(c_0_2350,plain,
    ( ti(X1,X2) = ti(X1,X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ order(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1501]) ).

cnf(c_0_2351,plain,
    ( ti(X1,X2) = ti(X1,X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ order(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1502]) ).

cnf(c_0_2352,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X2),top_top(fun(X1,bool))))
    | hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X2),top_top(fun(X1,bool))) != top_top(fun(X1,bool))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1503]) ).

cnf(c_0_2353,plain,
    ( hBOOL(X1)
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X3),X4))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X4),X3))
    | ~ preorder(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1504]) ).

cnf(c_0_2354,plain,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ linorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1505]) ).

cnf(c_0_2355,plain,
    ( ~ preorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1481]) ).

cnf(c_0_2356,plain,
    ( ~ linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1506]) ).

cnf(c_0_2357,plain,
    ( ~ linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1507]) ).

cnf(c_0_2358,plain,
    ( ~ linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1508]) ).

cnf(c_0_2359,plain,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ preorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1509]) ).

cnf(c_0_2360,plain,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ preorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1510]) ).

cnf(c_0_2361,plain,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ preorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1511]) ).

cnf(c_0_2362,plain,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ order(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1512]) ).

cnf(c_0_2363,plain,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ preorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1513]) ).

cnf(c_0_2364,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),hAPP(nat,nat,suc,X1)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | X2 != X1 ),
    inference(split_conjunct,[status(thm)],[c_0_1468]) ).

cnf(c_0_2365,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1490]) ).

cnf(c_0_2366,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1514]) ).

cnf(c_0_2367,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1515]) ).

cnf(c_0_2368,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1489]) ).

cnf(c_0_2369,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,suc,X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1516]) ).

cnf(c_0_2370,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,suc,X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1478]) ).

cnf(c_0_2371,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),one_one(X1)),one_one(X1))))
    | ~ linordered_semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1517]) ).

cnf(c_0_2372,plain,
    ( X1 = X2
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1518]) ).

cnf(c_0_2373,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),one_one(X1))))
    | ~ linordered_semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1519]) ).

cnf(c_0_2374,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4))
    | ~ comm_semiring_1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1520]) ).

cnf(c_0_2375,plain,
    ( hBOOL(hAPP(nat,bool,X3,X1))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,X3,X2))
    | ~ hBOOL(hAPP(nat,bool,X3,esk86_3(X3,X1,X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_1480]) ).

cnf(c_0_2376,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ dense_linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),esk37_3(X1,X3,X2)),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1521]) ).

cnf(c_0_2377,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X1,bool),nat,finite_card(X1),X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_1522]) ).

cnf(c_0_2378,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1523]) ).

cnf(c_0_2379,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1524]) ).

cnf(c_0_2380,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2))),
    inference(split_conjunct,[status(thm)],[c_0_1525]) ).

cnf(c_0_2381,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X1))),
    inference(split_conjunct,[status(thm)],[c_0_1526]) ).

cnf(c_0_2382,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | X1 = X2
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_1401]) ).

cnf(c_0_2383,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X3)),
    inference(split_conjunct,[status(thm)],[c_0_1527]) ).

cnf(c_0_2384,plain,
    ( hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,X1),X2))
    | hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,esk32_2(X1,X2)) != hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),esk32_2(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1320]) ).

cnf(c_0_2385,plain,
    ( hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
    | ~ hBOOL(hAPP(nat,bool,X1,X2))
    | ~ hBOOL(hAPP(nat,bool,X1,X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),esk81_2(X2,X1))) ),
    inference(split_conjunct,[status(thm)],[c_0_1528]) ).

cnf(c_0_2386,plain,
    ( hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
    | ~ hBOOL(hAPP(nat,bool,X1,X2))
    | ~ hBOOL(hAPP(nat,bool,X1,X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),esk79_2(X2,X1))) ),
    inference(split_conjunct,[status(thm)],[c_0_1497]) ).

cnf(c_0_2387,plain,
    ( hBOOL(hAPP(X1,bool,X2,X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X2))
    | ~ hBOOL(hAPP(X1,bool,X4,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1529]) ).

cnf(c_0_2388,plain,
    ( hBOOL(hAPP(X1,bool,X2,X3))
    | ~ hBOOL(hAPP(X1,bool,X4,X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1530]) ).

cnf(c_0_2389,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk72_2(X1,X2)),X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1531]) ).

cnf(c_0_2390,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | X2 != hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1532]) ).

cnf(c_0_2391,plain,
    hAPP(X1,X2,hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X1,fun(X3,X2)),fun(fun(X1,X3),fun(X1,X2)),combs(X1,X3,X2),X4),X5),X6) = hAPP(X3,X2,hAPP(X1,fun(X3,X2),X4,X6),hAPP(X1,X3,X5,X6)),
    inference(split_conjunct,[status(thm)],[c_0_1533]) ).

cnf(c_0_2392,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk53_3(X1,X3,X2)),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1484]) ).

cnf(c_0_2393,plain,
    ( X2 = hAPP(nat,nat,suc,X1)
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),esk93_2(X1,X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1534]) ).

cnf(c_0_2394,plain,
    ( X1 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),esk87_2(X2,X1)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_1535]) ).

cnf(c_0_2395,plain,
    ( X1 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),esk83_2(X2,X1)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_1532]) ).

cnf(c_0_2396,plain,
    ( X1 = zero_zero(nat)
    | X1 = hAPP(nat,nat,suc,esk85_2(X1,X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2))) ),
    inference(split_conjunct,[status(thm)],[c_0_1483]) ).

cnf(c_0_2397,plain,
    ( ti(X1,X2) = zero_zero(X1)
    | ~ ring_char_0(X1)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),ring_1_Ints(X1)))
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2) != zero_zero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1536]) ).

cnf(c_0_2398,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ti(X1,X3) != ti(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1500]) ).

cnf(c_0_2399,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | ti(X1,X3) != ti(X1,X4)
    | ~ order(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1537]) ).

cnf(c_0_2400,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ti(X1,X4) != ti(X1,X2)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
    | ~ order(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1538]) ).

cnf(c_0_2401,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ti(X1,X3) != ti(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1539]) ).

cnf(c_0_2402,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | ti(X1,X3) != ti(X1,X4)
    | ~ order(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1540]) ).

cnf(c_0_2403,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X4) != ti(X1,X2)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
    | ~ order(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1541]) ).

cnf(c_0_2404,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X3) = ti(X1,X2)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ order(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1542]) ).

cnf(c_0_2405,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X2) = ti(X1,X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ order(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1543]) ).

cnf(c_0_2406,plain,
    ( ti(X1,X2) = ti(X1,X3)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ order(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1544]) ).

cnf(c_0_2407,plain,
    ( ti(X1,X2) = ti(X1,X3)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1498]) ).

cnf(c_0_2408,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X3) = ti(X1,X2)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ order(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1545]) ).

cnf(c_0_2409,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X2) = ti(X1,X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ order(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1546]) ).

cnf(c_0_2410,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X2) = ti(X1,X3)
    | ~ linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1547]) ).

cnf(c_0_2411,plain,
    ( ti(X1,X2) = ti(X1,X3)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1548]) ).

cnf(c_0_2412,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X2) = ti(X1,X3)
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1549]) ).

cnf(c_0_2413,plain,
    ( ti(X1,X2) = ti(X1,X3)
    | hAPP(X1,X4,X5,X2) != hAPP(X1,X4,X5,X3)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X4),fun(fun(X1,bool),bool),inj_on(X1,X4),X5),top_top(fun(X1,bool)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1550]) ).

cnf(c_0_2414,plain,
    ( ti(X1,X4) = ti(X1,X5)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),top_top(fun(X1,bool))))
    | hAPP(X1,X2,X3,X4) != hAPP(X1,X2,X3,X5) ),
    inference(split_conjunct,[status(thm)],[c_0_1551]) ).

cnf(c_0_2415,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
    | X2 != X4
    | ~ ord(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1552]) ).

cnf(c_0_2416,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | X4 != X3
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | ~ ord(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1553]) ).

cnf(c_0_2417,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
    | X2 != X4
    | ~ ord(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1554]) ).

cnf(c_0_2418,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | X4 != X3
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | ~ ord(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1555]) ).

cnf(c_0_2419,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ preorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1556]) ).

cnf(c_0_2420,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1548]) ).

cnf(c_0_2421,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ preorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1481]) ).

cnf(c_0_2422,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1549]) ).

cnf(c_0_2423,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2)))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_1488]) ).

cnf(c_0_2424,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_1469]) ).

cnf(c_0_2425,plain,
    hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X1),X2))),
    inference(split_conjunct,[status(thm)],[c_0_1557]) ).

cnf(c_0_2426,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),esk82_2(X1,X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1558]) ).

cnf(c_0_2427,plain,
    hAPP(product_prod(X1,X2),X3,hAPP(fun(X1,fun(X2,X3)),fun(product_prod(X1,X2),X3),product_prod_rec(X1,X2,X3),X4),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X5),X6)) = hAPP(X2,X3,hAPP(X1,fun(X2,X3),X4,X5),X6),
    inference(split_conjunct,[status(thm)],[c_0_1559]) ).

cnf(c_0_2428,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | X1 = X2
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1560]) ).

cnf(c_0_2429,plain,
    ( X1 = X2
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1561]) ).

cnf(c_0_2430,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | X1 = X2
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1562]) ).

cnf(c_0_2431,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1563]) ).

cnf(c_0_2432,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1564]) ).

cnf(c_0_2433,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1565]) ).

cnf(c_0_2434,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1561]) ).

cnf(c_0_2435,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1562]) ).

cnf(c_0_2436,plain,
    ( X1 = zero_zero(nat)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,zero_zero(nat)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1566]) ).

cnf(c_0_2437,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),esk26_2(X1,X2)),arrow_2064824852le_Lin)) ),
    inference(split_conjunct,[status(thm)],[c_0_1373]) ).

cnf(c_0_2438,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X1,bool),nat,finite_card(X1),top_top(fun(X1,bool)))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1567]) ).

cnf(c_0_2439,plain,
    ( hAPP(X1,X2,X3,X4) = hAPP(X1,X2,X3,X5)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),top_top(fun(X1,bool))))
    | ti(X1,X4) != ti(X1,X5) ),
    inference(split_conjunct,[status(thm)],[c_0_1551]) ).

cnf(c_0_2440,plain,
    hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),esk66_0),arrow_2064824852le_Lin)),
    inference(split_conjunct,[status(thm)],[c_0_1568]) ).

cnf(c_0_2441,plain,
    hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),esk19_0),arrow_2064824852le_Lin)),
    inference(split_conjunct,[status(thm)],[c_0_1380]) ).

cnf(c_0_2442,plain,
    hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),esk18_0),arrow_2064824852le_Lin)),
    inference(split_conjunct,[status(thm)],[c_0_1381]) ).

cnf(c_0_2443,plain,
    hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),lba),arrow_2064824852le_Lin)),
    inference(split_conjunct,[status(thm)],[c_0_1569]) ).

cnf(c_0_2444,plain,
    hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),lab),arrow_2064824852le_Lin)),
    inference(split_conjunct,[status(thm)],[c_0_1570]) ).

cnf(c_0_2445,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2) = zero_zero(X1)
    | ~ ring_char_0(X1)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),ring_1_Ints(X1)))
    | ti(X1,X2) != zero_zero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1536]) ).

cnf(c_0_2446,plain,
    ( hBOOL(hAPP(nat,bool,X1,X2))
    | ~ hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
    | ~ hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,suc,esk98_2(X2,X1)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1571]) ).

cnf(c_0_2447,plain,
    ( hAPP(fun(sum_sum(X1,X2),bool),nat,finite_card(sum_sum(X1,X2)),hAPP(fun(X2,bool),fun(sum_sum(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X2,bool),fun(sum_sum(X1,X2),bool)),sum_Plus(X1,X2),X3),X4)) = zero_zero(nat)
    | hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1429]) ).

cnf(c_0_2448,plain,
    ( hAPP(fun(sum_sum(X1,X2),bool),nat,finite_card(sum_sum(X1,X2)),hAPP(fun(X2,bool),fun(sum_sum(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X2,bool),fun(sum_sum(X1,X2),bool)),sum_Plus(X1,X2),X3),X4)) = zero_zero(nat)
    | hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_1429]) ).

cnf(c_0_2449,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),esk37_3(X1,X3,X2)),X2))
    | ~ dense_linorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1521]) ).

cnf(c_0_2450,plain,
    hAPP(X1,X2,hAPP(X3,fun(X1,X2),hAPP(fun(X1,fun(X3,X2)),fun(X3,fun(X1,X2)),combc(X1,X3,X2),X4),X5),X6) = hAPP(X3,X2,hAPP(X1,fun(X3,X2),X4,X6),X5),
    inference(split_conjunct,[status(thm)],[c_0_1572]) ).

cnf(c_0_2451,plain,
    hAPP(X1,X2,hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),combb(X3,X2,X1),X4),X5),X6) = hAPP(X3,X2,X4,hAPP(X1,X3,X5,X6)),
    inference(split_conjunct,[status(thm)],[c_0_1573]) ).

cnf(c_0_2452,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | ti(X1,esk69_4(X2,X1,X3,X4)) != ti(X1,esk70_4(X2,X1,X3,X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_1476]) ).

cnf(c_0_2453,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | ti(X1,esk30_4(X1,X2,X3,X4)) != ti(X1,esk31_4(X1,X2,X3,X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_1389]) ).

cnf(c_0_2454,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,X1)),X2) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),
    inference(split_conjunct,[status(thm)],[c_0_1574]) ).

cnf(c_0_2455,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | hAPP(X1,X2,X3,esk69_4(X2,X1,X3,X4)) = hAPP(X1,X2,X3,esk70_4(X2,X1,X3,X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_1476]) ).

cnf(c_0_2456,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | hAPP(X1,X2,X3,esk30_4(X1,X2,X3,X4)) = hAPP(X1,X2,X3,esk31_4(X1,X2,X3,X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_1389]) ).

cnf(c_0_2457,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),esk99_3(X1,X2,X3)))
    | ~ linordered_field(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1379]) ).

cnf(c_0_2458,plain,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3))
    | ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1493]) ).

cnf(c_0_2459,plain,
    ( hBOOL(hAPP(X1,bool,X2,X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1575]) ).

cnf(c_0_2460,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),esk82_2(X1,X2)) = X2
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1558]) ).

cnf(c_0_2461,plain,
    ( X1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),esk60_2(X2,X1))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_1576]) ).

cnf(c_0_2462,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ linorder(X1)
    | ti(X1,X2) != ti(X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1547]) ).

cnf(c_0_2463,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ti(X1,X3) = ti(X1,X2)
    | ~ linordered_idom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1577]) ).

cnf(c_0_2464,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ti(X1,X3) = ti(X1,X2)
    | ~ linorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1578]) ).

cnf(c_0_2465,plain,
    ( ti(X1,X2) = ti(X1,X3)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ linorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1508]) ).

cnf(c_0_2466,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X3) = ti(X1,X2)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ linorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1579]) ).

cnf(c_0_2467,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X3) = ti(X1,X2)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ linorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1539]) ).

cnf(c_0_2468,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ti(X1,X3) = ti(X1,X2)
    | ~ linorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1580]) ).

cnf(c_0_2469,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X3) = ti(X1,X2)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ linorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1581]) ).

cnf(c_0_2470,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ linorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1582]) ).

cnf(c_0_2471,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ linorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1583]) ).

cnf(c_0_2472,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ linorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1584]) ).

cnf(c_0_2473,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ linorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1506]) ).

cnf(c_0_2474,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ linorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1507]) ).

cnf(c_0_2475,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ linorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1585]) ).

cnf(c_0_2476,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ linorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1586]) ).

cnf(c_0_2477,plain,
    ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X1))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk78_2(X2,X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1587]) ).

cnf(c_0_2478,plain,
    ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X1))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk76_2(X1,X2)),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1495]) ).

cnf(c_0_2479,plain,
    ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X1))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),esk74_2(X1,X2)),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1496]) ).

cnf(c_0_2480,plain,
    ( hBOOL(hAPP(fun(sum_sum(X1,X2),bool),bool,finite_finite_1(sum_sum(X1,X2)),top_top(fun(sum_sum(X1,X2),bool))))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),top_top(fun(X2,bool))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1588]) ).

cnf(c_0_2481,plain,
    ( hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,finite_finite_1(product_prod(X1,X2)),top_top(fun(product_prod(X1,X2),bool))))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),top_top(fun(X2,bool))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1589]) ).

cnf(c_0_2482,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1))
    | X2 = X1 ),
    inference(split_conjunct,[status(thm)],[c_0_1590]) ).

cnf(c_0_2483,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1))
    | X2 = X1 ),
    inference(split_conjunct,[status(thm)],[c_0_1591]) ).

cnf(c_0_2484,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_1592]) ).

cnf(c_0_2485,plain,
    ( ti(X2,X3) = ti(X2,X5)
    | hAPP(X1,product_prod(X2,X1),hAPP(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),X3),X4) != hAPP(X1,product_prod(X2,X1),hAPP(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),X5),X6) ),
    inference(split_conjunct,[status(thm)],[c_0_1593]) ).

cnf(c_0_2486,plain,
    ( ti(X1,X4) = ti(X1,X6)
    | hAPP(X1,product_prod(X2,X1),hAPP(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),X3),X4) != hAPP(X1,product_prod(X2,X1),hAPP(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),X5),X6) ),
    inference(split_conjunct,[status(thm)],[c_0_1593]) ).

cnf(c_0_2487,plain,
    ( ti(X2,X3) = ti(X2,X5)
    | hAPP(X1,product_prod(X2,X1),hAPP(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),X3),X4) != hAPP(X1,product_prod(X2,X1),hAPP(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),X5),X6) ),
    inference(split_conjunct,[status(thm)],[c_0_1594]) ).

cnf(c_0_2488,plain,
    ( ti(X1,X4) = ti(X1,X6)
    | hAPP(X1,product_prod(X2,X1),hAPP(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),X3),X4) != hAPP(X1,product_prod(X2,X1),hAPP(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),X5),X6) ),
    inference(split_conjunct,[status(thm)],[c_0_1594]) ).

cnf(c_0_2489,plain,
    ( hAPP(fun(X1,bool),nat,finite_card(X1),X2) = zero_zero(nat)
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk80_2(X1,X2)),X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1595]) ).

cnf(c_0_2490,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),hAPP(nat,nat,suc,X2)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),
    inference(split_conjunct,[status(thm)],[c_0_1596]) ).

cnf(c_0_2491,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,X1)),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),hAPP(nat,nat,suc,X2)),
    inference(split_conjunct,[status(thm)],[c_0_1597]) ).

cnf(c_0_2492,plain,
    ( X2 = hAPP(nat,nat,suc,X1)
    | X2 = hAPP(nat,nat,suc,esk93_2(X1,X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1534]) ).

cnf(c_0_2493,plain,
    ( hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),esk81_2(X2,X1)),X2))
    | ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1528]) ).

cnf(c_0_2494,plain,
    ( hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk79_2(X2,X1)),X2))
    | ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1497]) ).

cnf(c_0_2495,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,suc,X2)))
    | X1 != hAPP(nat,nat,suc,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1478]) ).

cnf(c_0_2496,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool))))
    | hAPP(fun(X2,bool),nat,finite_card(X2),top_top(fun(X2,bool))) = hAPP(nat,nat,suc,zero_zero(nat))
    | ~ hBOOL(hAPP(fun(fun(X1,X2),bool),bool,finite_finite_1(fun(X1,X2)),top_top(fun(fun(X1,X2),bool)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1598]) ).

cnf(c_0_2497,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),top_top(fun(X1,bool))))
    | hAPP(X1,X2,X3,esk35_3(X1,X2,X3)) = hAPP(X1,X2,X3,esk36_3(X1,X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1599]) ).

cnf(c_0_2498,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk28_0),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool))))),
    inference(split_conjunct,[status(thm)],[c_0_1223]) ).

cnf(c_0_2499,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk27_0),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool))))),
    inference(split_conjunct,[status(thm)],[c_0_1224]) ).

cnf(c_0_2500,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),n),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool))))),
    inference(split_conjunct,[status(thm)],[c_0_1600]) ).

cnf(c_0_2501,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | X2 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1576]) ).

cnf(c_0_2502,plain,
    ( hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
    | hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,suc,esk97_1(X1))))
    | ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1601]) ).

cnf(c_0_2503,plain,
    ( X1 = hAPP(nat,nat,suc,esk88_1(X1))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_1602]) ).

cnf(c_0_2504,plain,
    ( X1 = hAPP(nat,nat,suc,esk84_1(X1))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_1603]) ).

cnf(c_0_2505,plain,
    hAPP(fun(arrow_660593299e_indi,bool),fun(nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(fun(arrow_660593299e_indi,bool),fun(nat,bool)),image(arrow_660593299e_indi,nat),esk100_0),top_top(fun(arrow_660593299e_indi,bool))) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool)))),
    inference(split_conjunct,[status(thm)],[c_0_1604]) ).

cnf(c_0_2506,plain,
    hAPP(fun(arrow_660593299e_indi,bool),fun(nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(fun(arrow_660593299e_indi,bool),fun(nat,bool)),image(arrow_660593299e_indi,nat),h),top_top(fun(arrow_660593299e_indi,bool))) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool)))),
    inference(split_conjunct,[status(thm)],[c_0_1605]) ).

cnf(c_0_2507,plain,
    hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X3),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),top_top(fun(X2,bool)))) = top_top(fun(fun(X1,X2),bool)),
    inference(split_conjunct,[status(thm)],[c_0_1606]) ).

cnf(c_0_2508,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,X3,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1575]) ).

cnf(c_0_2509,plain,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),zero_zero(X1)))
    | ~ linordered_semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1607]) ).

cnf(c_0_2510,plain,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),one_one(X1)),zero_zero(X1)))
    | ~ linordered_semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1608]) ).

cnf(c_0_2511,plain,
    ( ti(X1,X2) = top_top(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),top_top(X1)),X2))
    | ~ top(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1609]) ).

cnf(c_0_2512,plain,
    ( ti(X1,X2) = top_top(X1)
    | ~ top(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),top_top(X1)),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1610]) ).

cnf(c_0_2513,plain,
    ( ti(X1,X2) = ti(X1,X3)
    | ~ cancel_semigroup_add(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X2) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1611]) ).

cnf(c_0_2514,plain,
    ( ti(X1,X2) = ti(X1,X3)
    | ~ cancel_semigroup_add(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1612]) ).

cnf(c_0_2515,plain,
    ( ti(X1,X2) = ti(X1,X3)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X2) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)
    | ~ cancel_semigroup_add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1613]) ).

cnf(c_0_2516,plain,
    ( ti(X1,X2) = ti(X1,X3)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X2) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)
    | ~ cancel146912293up_add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1614]) ).

cnf(c_0_2517,plain,
    ( ti(X1,X2) = ti(X1,X3)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)
    | ~ cancel_semigroup_add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1615]) ).

cnf(c_0_2518,plain,
    ( ~ top(X1)
    | ti(X1,X2) != top_top(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),top_top(X1))) ),
    inference(split_conjunct,[status(thm)],[c_0_1616]) ).

cnf(c_0_2519,plain,
    ( ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X2) != ti(X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1549]) ).

cnf(c_0_2520,plain,
    ( ~ linorder(X1)
    | ti(X1,X2) != ti(X1,X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1578]) ).

cnf(c_0_2521,plain,
    ( ~ linorder(X1)
    | ti(X1,X2) != ti(X1,X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1578]) ).

cnf(c_0_2522,plain,
    ( ~ linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X2) != ti(X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1508]) ).

cnf(c_0_2523,plain,
    ( ti(X1,X2) != ti(X1,X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ order(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1617]) ).

cnf(c_0_2524,plain,
    ( ti(X1,X2) != ti(X1,X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ order(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1618]) ).

cnf(c_0_2525,plain,
    ( ti(X1,X2) != ti(X1,X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ order(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1619]) ).

cnf(c_0_2526,plain,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),top_top(X1)),X2))
    | ~ top(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1620]) ).

cnf(c_0_2527,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,zero_zero(nat))))
    | X1 != zero_zero(nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1566]) ).

cnf(c_0_2528,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,X1))),
    inference(split_conjunct,[status(thm)],[c_0_1621]) ).

cnf(c_0_2529,plain,
    ( ti(X1,X2) = ti(X1,X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),fequal(X1),X2),X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1622]) ).

cnf(c_0_2530,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2)))
    | X1 != zero_zero(nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1483]) ).

cnf(c_0_2531,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2)))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_1489]) ).

cnf(c_0_2532,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X1))),
    inference(split_conjunct,[status(thm)],[c_0_1623]) ).

cnf(c_0_2533,plain,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X2))
    | ~ preorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1624]) ).

cnf(c_0_2534,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),top_top(fun(X1,bool))))
    | ti(X1,esk35_3(X1,X2,X3)) != ti(X1,esk36_3(X1,X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_1599]) ).

cnf(c_0_2535,plain,
    ( X1 != zero_zero(nat)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_1625]) ).

cnf(c_0_2536,plain,
    ( X1 = zero_zero(nat)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),zero_zero(nat))) ),
    inference(split_conjunct,[status(thm)],[c_0_1626]) ).

cnf(c_0_2537,plain,
    ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),zero_zero(nat))),
    inference(split_conjunct,[status(thm)],[c_0_1627]) ).

cnf(c_0_2538,plain,
    ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),zero_zero(nat))),
    inference(split_conjunct,[status(thm)],[c_0_1628]) ).

cnf(c_0_2539,plain,
    ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),zero_zero(nat))),
    inference(split_conjunct,[status(thm)],[c_0_1629]) ).

cnf(c_0_2540,plain,
    ( X1 != zero_zero(nat)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_1630]) ).

cnf(c_0_2541,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_1562]) ).

cnf(c_0_2542,plain,
    ( X1 != X2
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1631]) ).

cnf(c_0_2543,plain,
    ( X1 != X2
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_1632]) ).

cnf(c_0_2544,plain,
    ( X1 != X2
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1591]) ).

cnf(c_0_2545,plain,
    ( X1 != X2
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_1591]) ).

cnf(c_0_2546,plain,
    ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X1)),
    inference(split_conjunct,[status(thm)],[c_0_1633]) ).

cnf(c_0_2547,plain,
    ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X1)),
    inference(split_conjunct,[status(thm)],[c_0_1634]) ).

cnf(c_0_2548,plain,
    ( X1 = X2
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X3) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1635]) ).

cnf(c_0_2549,plain,
    ( X1 = X2
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X1) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1636]) ).

cnf(c_0_2550,plain,
    ( hBOOL(X1)
    | hBOOL(X2)
    | ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_1637]) ).

cnf(c_0_2551,plain,
    ( hBOOL(X1)
    | ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X2),X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_1638]) ).

cnf(c_0_2552,plain,
    ( hBOOL(X1)
    | ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1639]) ).

cnf(c_0_2553,plain,
    ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X1))
    | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),esk78_2(X2,X1)),X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_1587]) ).

cnf(c_0_2554,plain,
    ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X1))
    | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),esk76_2(X1,X2)),X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_1495]) ).

cnf(c_0_2555,plain,
    ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X1))
    | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),esk74_2(X1,X2)),X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_1496]) ).

cnf(c_0_2556,plain,
    ( ti(fun(X1,X2),X3) = ti(fun(X1,X2),X4)
    | hAPP(X1,X2,X3,esk20_4(X1,X2,X3,X4)) != hAPP(X1,X2,X4,esk20_4(X1,X2,X3,X4)) ),
    inference(split_conjunct,[status(thm)],[c_0_1640]) ).

cnf(c_0_2557,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool))))
    | ~ hBOOL(hAPP(fun(fun(X2,X1),bool),bool,finite_finite_1(fun(X2,X1)),top_top(fun(fun(X2,X1),bool)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1641]) ).

cnf(c_0_2558,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool))))
    | ~ hBOOL(hAPP(fun(sum_sum(X1,X2),bool),bool,finite_finite_1(sum_sum(X1,X2)),top_top(fun(sum_sum(X1,X2),bool)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1588]) ).

cnf(c_0_2559,plain,
    ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),top_top(fun(X2,bool))))
    | ~ hBOOL(hAPP(fun(sum_sum(X1,X2),bool),bool,finite_finite_1(sum_sum(X1,X2)),top_top(fun(sum_sum(X1,X2),bool)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1588]) ).

cnf(c_0_2560,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1449]) ).

cnf(c_0_2561,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X2))
    | ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1449]) ).

cnf(c_0_2562,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1642]) ).

cnf(c_0_2563,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ti(fun(X1,bool),X3) != ti(fun(X1,bool),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1643]) ).

cnf(c_0_2564,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1644]) ).

cnf(c_0_2565,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X2))
    | ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1644]) ).

cnf(c_0_2566,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1492]) ).

cnf(c_0_2567,plain,
    hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),top_top(fun(X1,bool)))),
    inference(split_conjunct,[status(thm)],[c_0_1645]) ).

cnf(c_0_2568,plain,
    hAPP(X1,X1,hAPP(X1,fun(X1,X1),hAPP(bool,fun(X1,fun(X1,X1)),if(X1),fFalse),X2),X3) = ti(X1,X3),
    inference(split_conjunct,[status(thm)],[c_0_1646]) ).

cnf(c_0_2569,plain,
    hAPP(X1,X1,hAPP(X1,fun(X1,X1),hAPP(bool,fun(X1,fun(X1,X1)),if(X1),fTrue),X2),X3) = ti(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_1647]) ).

cnf(c_0_2570,plain,
    ( X1 = hAPP(nat,nat,suc,zero_zero(nat))
    | X2 = hAPP(nat,nat,suc,zero_zero(nat))
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) != hAPP(nat,nat,suc,zero_zero(nat)) ),
    inference(split_conjunct,[status(thm)],[c_0_1648]) ).

cnf(c_0_2571,plain,
    ( X1 = hAPP(nat,nat,suc,zero_zero(nat))
    | X2 = hAPP(nat,nat,suc,zero_zero(nat))
    | hAPP(nat,nat,suc,zero_zero(nat)) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1649]) ).

cnf(c_0_2572,plain,
    hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X2)),
    inference(split_conjunct,[status(thm)],[c_0_1650]) ).

cnf(c_0_2573,plain,
    ( hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
    | ~ hBOOL(hAPP(nat,bool,X1,X2))
    | ~ hBOOL(hAPP(nat,bool,X1,esk97_1(X1))) ),
    inference(split_conjunct,[status(thm)],[c_0_1601]) ).

cnf(c_0_2574,plain,
    ( ti(fun(X1,bool),X2) = top_top(fun(X1,bool))
    | hAPP(fun(X1,bool),nat,finite_card(X1),X2) != hAPP(fun(X1,bool),nat,finite_card(X1),top_top(fun(X1,bool)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1651]) ).

cnf(c_0_2575,plain,
    ( hAPP(X1,product_prod(X2,X1),hAPP(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),X3),X4) = hAPP(X1,product_prod(X2,X1),hAPP(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),X5),X6)
    | ti(X1,X4) != ti(X1,X6)
    | ti(X2,X3) != ti(X2,X5) ),
    inference(split_conjunct,[status(thm)],[c_0_1593]) ).

cnf(c_0_2576,plain,
    hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),combi(X1)),X2)),
    inference(split_conjunct,[status(thm)],[c_0_1652]) ).

cnf(c_0_2577,plain,
    hBOOL(hAPP(fun(arrow_660593299e_indi,bool),bool,hAPP(fun(arrow_660593299e_indi,nat),fun(fun(arrow_660593299e_indi,bool),bool),inj_on(arrow_660593299e_indi,nat),esk100_0),top_top(fun(arrow_660593299e_indi,bool)))),
    inference(split_conjunct,[status(thm)],[c_0_1604]) ).

cnf(c_0_2578,plain,
    hBOOL(hAPP(fun(arrow_660593299e_indi,bool),bool,hAPP(fun(arrow_660593299e_indi,nat),fun(fun(arrow_660593299e_indi,bool),bool),inj_on(arrow_660593299e_indi,nat),h),top_top(fun(arrow_660593299e_indi,bool)))),
    inference(split_conjunct,[status(thm)],[c_0_1653]) ).

cnf(c_0_2579,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
    | X1 != hAPP(nat,nat,suc,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1603]) ).

cnf(c_0_2580,plain,
    ti(fun(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool)))),finite908156982e_idem(X1,X2)) = finite908156982e_idem(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_1654]) ).

cnf(c_0_2581,plain,
    hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),top_top(fun(X1,bool)))),
    inference(split_conjunct,[status(thm)],[c_0_1655]) ).

cnf(c_0_2582,plain,
    hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),top_top(fun(X1,bool)))),
    inference(split_conjunct,[status(thm)],[c_0_1656]) ).

cnf(c_0_2583,plain,
    hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,nat),fun(fun(nat,bool),bool),inj_on(nat,nat),suc),X1)),
    inference(split_conjunct,[status(thm)],[c_0_1657]) ).

cnf(c_0_2584,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),one_one(X1)),ring_1_Ints(X1)))
    | ~ ring_1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1658]) ).

cnf(c_0_2585,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),zero_zero(X1)),ring_1_Ints(X1)))
    | ~ ring_1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1659]) ).

cnf(c_0_2586,plain,
    ( X1 = hAPP(nat,nat,suc,zero_zero(nat))
    | X1 = zero_zero(nat)
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) != hAPP(nat,nat,suc,zero_zero(nat)) ),
    inference(split_conjunct,[status(thm)],[c_0_1648]) ).

cnf(c_0_2587,plain,
    ( X2 = zero_zero(nat)
    | X2 = hAPP(nat,nat,suc,zero_zero(nat))
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) != hAPP(nat,nat,suc,zero_zero(nat)) ),
    inference(split_conjunct,[status(thm)],[c_0_1648]) ).

cnf(c_0_2588,plain,
    ( X1 = hAPP(nat,nat,suc,zero_zero(nat))
    | X1 = zero_zero(nat)
    | hAPP(nat,nat,suc,zero_zero(nat)) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1649]) ).

cnf(c_0_2589,plain,
    ( X2 = zero_zero(nat)
    | X2 = hAPP(nat,nat,suc,zero_zero(nat))
    | hAPP(nat,nat,suc,zero_zero(nat)) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1649]) ).

cnf(c_0_2590,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool))))
    | ~ hBOOL(hAPP(fun(option(X1),bool),bool,finite_finite_1(option(X1)),top_top(fun(option(X1),bool)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1660]) ).

cnf(c_0_2591,plain,
    ( hBOOL(hAPP(nat,bool,X1,X2))
    | hBOOL(hAPP(nat,bool,X1,esk98_2(X2,X1)))
    | ~ hBOOL(hAPP(nat,bool,X1,zero_zero(nat))) ),
    inference(split_conjunct,[status(thm)],[c_0_1571]) ).

cnf(c_0_2592,plain,
    ( hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
    | hBOOL(hAPP(nat,bool,X1,esk81_2(X2,X1)))
    | ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1528]) ).

cnf(c_0_2593,plain,
    ( hBOOL(hAPP(fun(option(X1),bool),bool,finite_finite_1(option(X1)),top_top(fun(option(X1),bool))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool)))) ),
    inference(split_conjunct,[status(thm)],[c_0_1660]) ).

cnf(c_0_2594,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)
    | ~ cancel_semigroup_add(X1)
    | ti(X1,X3) != ti(X1,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1611]) ).

cnf(c_0_2595,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)
    | ~ cancel_semigroup_add(X1)
    | ti(X1,X2) != ti(X1,X4) ),
    inference(split_conjunct,[status(thm)],[c_0_1612]) ).

cnf(c_0_2596,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),top_top(X1)),X2))
    | ~ top(X1)
    | ti(X1,X2) != top_top(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1610]) ).

cnf(c_0_2597,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ order(X1)
    | ti(X1,X2) != ti(X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1548]) ).

cnf(c_0_2598,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ order(X1)
    | ti(X1,X2) != ti(X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1499]) ).

cnf(c_0_2599,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ order(X1)
    | ti(X1,X2) != ti(X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1499]) ).

cnf(c_0_2600,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),fequal(X1),X2),X3))
    | ti(X1,X2) != ti(X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_1661]) ).

cnf(c_0_2601,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),one_one(X1)))
    | ~ linordered_semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1662]) ).

cnf(c_0_2602,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),one_one(X1)))
    | ~ linordered_semidom(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1663]) ).

cnf(c_0_2603,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),top_top(X1)))
    | ti(X1,X2) = top_top(X1)
    | ~ top(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1616]) ).

cnf(c_0_2604,plain,
    ( X2 = zero_zero(nat)
    | X1 = zero_zero(nat)
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) != hAPP(nat,nat,suc,zero_zero(nat)) ),
    inference(split_conjunct,[status(thm)],[c_0_1648]) ).

cnf(c_0_2605,plain,
    ( X2 = zero_zero(nat)
    | X1 = zero_zero(nat)
    | hAPP(nat,nat,suc,zero_zero(nat)) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1649]) ).

cnf(c_0_2606,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X2)
    | ~ comm_semiring_1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1664]) ).

cnf(c_0_2607,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),top_top(X1)))
    | ~ top(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1665]) ).

cnf(c_0_2608,plain,
    hAPP(fun(X1,bool),fun(sum_sum(X2,X1),bool),hAPP(fun(X2,bool),fun(fun(X1,bool),fun(sum_sum(X2,X1),bool)),sum_Plus(X2,X1),top_top(fun(X2,bool))),top_top(fun(X1,bool))) = top_top(fun(sum_sum(X2,X1),bool)),
    inference(split_conjunct,[status(thm)],[c_0_1666]) ).

cnf(c_0_2609,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | X2 != X3
    | ~ preorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1667]) ).

cnf(c_0_2610,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X2))
    | ~ preorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1668]) ).

cnf(c_0_2611,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
    | X1 = zero_zero(nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1625]) ).

cnf(c_0_2612,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
    | X1 = zero_zero(nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1669]) ).

cnf(c_0_2613,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),X1)),
    inference(split_conjunct,[status(thm)],[c_0_1670]) ).

cnf(c_0_2614,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),X1)),
    inference(split_conjunct,[status(thm)],[c_0_1671]) ).

cnf(c_0_2615,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),zero_zero(nat)))
    | X1 != zero_zero(nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1626]) ).

cnf(c_0_2616,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_1564]) ).

cnf(c_0_2617,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_1561]) ).

cnf(c_0_2618,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_1672]) ).

cnf(c_0_2619,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X2)
    | X1 != X3 ),
    inference(split_conjunct,[status(thm)],[c_0_1635]) ).

cnf(c_0_2620,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X3)
    | X2 != X3 ),
    inference(split_conjunct,[status(thm)],[c_0_1636]) ).

cnf(c_0_2621,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X1)),
    inference(split_conjunct,[status(thm)],[c_0_1673]) ).

cnf(c_0_2622,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X1),
    inference(split_conjunct,[status(thm)],[c_0_1674]) ).

cnf(c_0_2623,plain,
    ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X1),X2))
    | ~ hBOOL(X2)
    | ~ hBOOL(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1675]) ).

cnf(c_0_2624,plain,
    ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X1),X2))
    | ~ hBOOL(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1676]) ).

cnf(c_0_2625,plain,
    ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X1),X2))
    | ~ hBOOL(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1677]) ).

cnf(c_0_2626,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) = hAPP(nat,nat,suc,zero_zero(nat))
    | X2 != zero_zero(nat)
    | X1 != hAPP(nat,nat,suc,zero_zero(nat)) ),
    inference(split_conjunct,[status(thm)],[c_0_1648]) ).

cnf(c_0_2627,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) = hAPP(nat,nat,suc,zero_zero(nat))
    | X2 != hAPP(nat,nat,suc,zero_zero(nat))
    | X1 != zero_zero(nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1648]) ).

cnf(c_0_2628,plain,
    ( hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)
    | X2 != zero_zero(nat)
    | X1 != hAPP(nat,nat,suc,zero_zero(nat)) ),
    inference(split_conjunct,[status(thm)],[c_0_1649]) ).

cnf(c_0_2629,plain,
    ( hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)
    | X2 != hAPP(nat,nat,suc,zero_zero(nat))
    | X1 != zero_zero(nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1649]) ).

cnf(c_0_2630,plain,
    hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,f)),
    inference(split_conjunct,[status(thm)],[c_0_1678]) ).

cnf(c_0_2631,plain,
    hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,f)),
    inference(split_conjunct,[status(thm)],[c_0_1679]) ).

cnf(c_0_2632,plain,
    ( ti(X1,X2) = zero_zero(X1)
    | ~ semiri456707255roduct(X1)
    | ti(X1,X3) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1680]) ).

cnf(c_0_2633,plain,
    ( ti(X1,X2) = zero_zero(X1)
    | ~ linord219039673up_add(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2) != zero_zero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1681]) ).

cnf(c_0_2634,plain,
    ( ti(X1,X2) = zero_zero(X1)
    | ~ linord219039673up_add(X1)
    | zero_zero(X1) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1682]) ).

cnf(c_0_2635,plain,
    ( X1 = zero_zero(nat)
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) != zero_zero(nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1683]) ).

cnf(c_0_2636,plain,
    ( X2 = zero_zero(nat)
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) != zero_zero(nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1683]) ).

cnf(c_0_2637,plain,
    ( X1 = zero_zero(nat)
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X1) != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_1684]) ).

cnf(c_0_2638,plain,
    hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),combi(X1)),X2) = ti(fun(X1,bool),X2),
    inference(split_conjunct,[status(thm)],[c_0_1685]) ).

cnf(c_0_2639,plain,
    ( hAPP(fun(X1,bool),nat,finite_card(X1),X2) = zero_zero(nat)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | one_one(nat) != zero_zero(nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1595]) ).

cnf(c_0_2640,plain,
    hAPP(nat,nat,suc,X1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),X1),
    inference(split_conjunct,[status(thm)],[c_0_1686]) ).

cnf(c_0_2641,plain,
    hAPP(nat,nat,suc,X1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),one_one(nat)),
    inference(split_conjunct,[status(thm)],[c_0_1687]) ).

cnf(c_0_2642,plain,
    hAPP(nat,fun(nat,bool),ord_less(nat),X1) = hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),
    inference(split_conjunct,[status(thm)],[c_0_1688]) ).

cnf(c_0_2643,plain,
    ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),top_top(fun(nat,bool)))),
    inference(split_conjunct,[status(thm)],[c_0_1689]) ).

cnf(c_0_2644,plain,
    ti(fun(fun(nat,fun(nat,nat)),fun(fun(X1,nat),fun(nat,fun(fun(X1,bool),nat)))),finite_fold_image(nat,X1)) = finite_fold_image(nat,X1),
    inference(split_conjunct,[status(thm)],[c_0_1690]) ).

cnf(c_0_2645,plain,
    ti(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool)),arrow_218898985ctator) = arrow_218898985ctator,
    inference(split_conjunct,[status(thm)],[c_0_1691]) ).

cnf(c_0_2646,plain,
    ti(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),arrow_831799591nimity) = arrow_831799591nimity,
    inference(split_conjunct,[status(thm)],[c_0_1692]) ).

cnf(c_0_2647,plain,
    ti(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),arrow_2037941124le_IIA) = arrow_2037941124le_IIA,
    inference(split_conjunct,[status(thm)],[c_0_1693]) ).

cnf(c_0_2648,plain,
    top_top(fun(X1,bool)) = hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(bool,fun(X1,bool),combk(bool,X1),fTrue)),
    inference(split_conjunct,[status(thm)],[c_0_1694]) ).

cnf(c_0_2649,plain,
    hAPP(X1,X2,hAPP(X2,fun(X1,X2),combk(X2,X1),X3),X4) = ti(X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_1695]) ).

cnf(c_0_2650,plain,
    ( ti(X1,X2) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)
    | ~ semiri456707255roduct(X1)
    | ti(X1,X3) != zero_zero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1680]) ).

cnf(c_0_2651,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2) = zero_zero(X1)
    | ~ linord219039673up_add(X1)
    | ti(X1,X2) != zero_zero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1681]) ).

cnf(c_0_2652,plain,
    ( zero_zero(X1) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)
    | ~ linord219039673up_add(X1)
    | ti(X1,X2) != zero_zero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1682]) ).

cnf(c_0_2653,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),zero_zero(X1)),X2) = ti(X1,X2)
    | ~ comm_semiring_1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1696]) ).

cnf(c_0_2654,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),zero_zero(X1)),X2) = ti(X1,X2)
    | ~ monoid_add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1697]) ).

cnf(c_0_2655,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),zero_zero(X1)),X2) = ti(X1,X2)
    | ~ comm_monoid_add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1698]) ).

cnf(c_0_2656,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),zero_zero(X1)) = ti(X1,X2)
    | ~ comm_semiring_1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1699]) ).

cnf(c_0_2657,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),zero_zero(X1)) = ti(X1,X2)
    | ~ monoid_add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1700]) ).

cnf(c_0_2658,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),zero_zero(X1)) = ti(X1,X2)
    | ~ comm_monoid_add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1701]) ).

cnf(c_0_2659,plain,
    ( hAPP(fun(X1,bool),nat,finite_card(X1),X2) = zero_zero(nat)
    | hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1355]) ).

cnf(c_0_2660,plain,
    ( hAPP(fun(X1,bool),nat,finite_card(X1),X2) = zero_zero(nat)
    | hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_1702]) ).

cnf(c_0_2661,plain,
    ti(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),arrow_1322701812_below) = arrow_1322701812_below,
    inference(split_conjunct,[status(thm)],[c_0_1703]) ).

cnf(c_0_2662,plain,
    ti(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),arrow_14103264_above) = arrow_14103264_above,
    inference(split_conjunct,[status(thm)],[c_0_1704]) ).

cnf(c_0_2663,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) = zero_zero(nat)
    | X2 != zero_zero(nat)
    | X1 != zero_zero(nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1683]) ).

cnf(c_0_2664,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_1705]) ).

cnf(c_0_2665,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),zero_zero(nat)) = X1,
    inference(split_conjunct,[status(thm)],[c_0_1706]) ).

cnf(c_0_2666,plain,
    ( ~ hBOOL(X1)
    | ~ hBOOL(hAPP(bool,bool,fNot,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_1707]) ).

cnf(c_0_2667,plain,
    ( X1 = X2
    | hAPP(nat,nat,suc,X1) != hAPP(nat,nat,suc,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1708]) ).

cnf(c_0_2668,plain,
    ( X1 = X2
    | hAPP(nat,nat,suc,X1) != hAPP(nat,nat,suc,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1709]) ).

cnf(c_0_2669,plain,
    ti(fun(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool))),pi(X1,X2)) = pi(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_1710]) ).

cnf(c_0_2670,plain,
    ti(X1,hAPP(X2,X1,X3,X4)) = hAPP(X2,X1,X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_1711]) ).

cnf(c_0_2671,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool))))
    | ~ finite_finite(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1712]) ).

cnf(c_0_2672,plain,
    hBOOL(hAPP(fun(arrow_660593299e_indi,bool),bool,finite_finite_1(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool)))),
    inference(split_conjunct,[status(thm)],[c_0_1713]) ).

cnf(c_0_2673,plain,
    ti(fun(fun(X1,fun(X2,X3)),fun(fun(X1,X2),fun(X1,X3))),combs(X1,X2,X3)) = combs(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_1714]) ).

cnf(c_0_2674,plain,
    hBOOL(hAPP(X1,bool,top_top(fun(X1,bool)),X2)),
    inference(split_conjunct,[status(thm)],[c_0_1715]) ).

cnf(c_0_2675,plain,
    hAPP(X1,X2,ti(fun(X1,X2),X3),X4) = hAPP(X1,X2,X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_1716]) ).

cnf(c_0_2676,plain,
    ti(fun(fun(X1,bool),fun(fun(X2,bool),fun(sum_sum(X1,X2),bool))),sum_Plus(X1,X2)) = sum_Plus(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_1717]) ).

cnf(c_0_2677,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ finite_finite(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1718]) ).

cnf(c_0_2678,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ finite_finite(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1719]) ).

cnf(c_0_2679,plain,
    hAPP(X1,X2,X3,ti(X1,X4)) = hAPP(X1,X2,X3,X4),
    inference(split_conjunct,[status(thm)],[c_0_1720]) ).

cnf(c_0_2680,plain,
    ti(fun(fun(X1,fun(X2,X3)),fun(product_prod(X1,X2),X3)),product_prod_rec(X1,X2,X3)) = product_prod_rec(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_1721]) ).

cnf(c_0_2681,plain,
    ti(fun(fun(X1,fun(X2,X3)),fun(X2,fun(X1,X3))),combc(X1,X2,X3)) = combc(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_1722]) ).

cnf(c_0_2682,plain,
    ti(fun(fun(X1,X2),fun(fun(X3,X1),fun(X3,X2))),combb(X1,X2,X3)) = combb(X1,X2,X3),
    inference(split_conjunct,[status(thm)],[c_0_1723]) ).

cnf(c_0_2683,plain,
    ( hBOOL(hAPP(bool,bool,fNot,X1))
    | hBOOL(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1724]) ).

cnf(c_0_2684,plain,
    ( hAPP(nat,nat,suc,X1) = hAPP(nat,nat,suc,X2)
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[c_0_1708]) ).

cnf(c_0_2685,plain,
    ti(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1427655034_mktop) = arrow_1427655034_mktop,
    inference(split_conjunct,[status(thm)],[c_0_1725]) ).

cnf(c_0_2686,plain,
    ti(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1278947948_mkbot) = arrow_1278947948_mkbot,
    inference(split_conjunct,[status(thm)],[c_0_1726]) ).

cnf(c_0_2687,plain,
    zero_zero(nat) != hAPP(nat,nat,suc,X1),
    inference(split_conjunct,[status(thm)],[c_0_1727]) ).

cnf(c_0_2688,plain,
    zero_zero(nat) != hAPP(nat,nat,suc,X1),
    inference(split_conjunct,[status(thm)],[c_0_1728]) ).

cnf(c_0_2689,plain,
    hAPP(nat,nat,suc,X1) != zero_zero(nat),
    inference(split_conjunct,[status(thm)],[c_0_1729]) ).

cnf(c_0_2690,plain,
    hAPP(nat,nat,suc,X1) != zero_zero(nat),
    inference(split_conjunct,[status(thm)],[c_0_1730]) ).

cnf(c_0_2691,plain,
    zero_zero(nat) != hAPP(nat,nat,suc,X1),
    inference(split_conjunct,[status(thm)],[c_0_1731]) ).

cnf(c_0_2692,plain,
    hAPP(nat,nat,suc,X1) != zero_zero(nat),
    inference(split_conjunct,[status(thm)],[c_0_1732]) ).

cnf(c_0_2693,plain,
    ti(fun(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1))),hilbert_inv_into(X1,X2)) = hilbert_inv_into(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_1733]) ).

cnf(c_0_2694,plain,
    X1 != hAPP(nat,nat,suc,X1),
    inference(split_conjunct,[status(thm)],[c_0_1734]) ).

cnf(c_0_2695,plain,
    hAPP(nat,nat,suc,X1) != X1,
    inference(split_conjunct,[status(thm)],[c_0_1735]) ).

cnf(c_0_2696,plain,
    ti(fun(fun(product_prod(X1,X2),bool),fun(X1,fun(X2,bool))),in_rel(X1,X2)) = in_rel(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_1736]) ).

cnf(c_0_2697,plain,
    ti(fun(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool))),image(X1,X2)) = image(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_1737]) ).

cnf(c_0_2698,plain,
    hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2) = ti(fun(X1,bool),X2),
    inference(split_conjunct,[status(thm)],[c_0_1738]) ).

cnf(c_0_2699,plain,
    ti(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),arrow_1111136790e_Prof) = arrow_1111136790e_Prof,
    inference(split_conjunct,[status(thm)],[c_0_1739]) ).

cnf(c_0_2700,plain,
    hAPP(fun(product_unit,bool),nat,finite_card(product_unit),top_top(fun(product_unit,bool))) = one_one(nat),
    inference(split_conjunct,[status(thm)],[c_0_1740]) ).

cnf(c_0_2701,plain,
    ( hAPP(X1,X2,top_top(fun(X1,X2)),X3) = top_top(X2)
    | ~ top(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1741]) ).

cnf(c_0_2702,plain,
    ti(fun(fun(X1,X2),fun(fun(X1,bool),bool)),inj_on(X1,X2)) = inj_on(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_1742]) ).

cnf(c_0_2703,plain,
    hAPP(X1,X1,combi(X1),X2) = ti(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_1743]) ).

cnf(c_0_2704,plain,
    ( X1 = hAPP(nat,nat,suc,esk96_1(X1))
    | X1 = zero_zero(nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1744]) ).

cnf(c_0_2705,plain,
    ( X1 = hAPP(nat,nat,suc,esk95_1(X1))
    | X1 = zero_zero(nat) ),
    inference(split_conjunct,[status(thm)],[c_0_1745]) ).

cnf(c_0_2706,plain,
    one_one(nat) = hAPP(nat,nat,suc,zero_zero(nat)),
    inference(split_conjunct,[status(thm)],[c_0_1746]) ).

cnf(c_0_2707,plain,
    ti(fun(X1,fun(X2,product_prod(X1,X2))),product_Pair(X1,X2)) = product_Pair(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_1747]) ).

cnf(c_0_2708,plain,
    ti(fun(bool,fun(X1,fun(X1,X1))),if(X1)) = if(X1),
    inference(split_conjunct,[status(thm)],[c_0_1748]) ).

cnf(c_0_2709,plain,
    ( ti(fun(X1,fun(X1,fun(X1,bool))),ord_atLeastLessThan(X1)) = ord_atLeastLessThan(X1)
    | ~ linorder(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1749]) ).

cnf(c_0_2710,plain,
    ti(fun(X1,fun(fun(X1,bool),bool)),member(X1)) = member(X1),
    inference(split_conjunct,[status(thm)],[c_0_1750]) ).

cnf(c_0_2711,plain,
    ti(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),arrow_2064824852le_Lin) = arrow_2064824852le_Lin,
    inference(split_conjunct,[status(thm)],[c_0_1751]) ).

cnf(c_0_2712,plain,
    ti(fun(fun(X1,bool),fun(X1,bool)),collect(X1)) = collect(X1),
    inference(split_conjunct,[status(thm)],[c_0_1752]) ).

cnf(c_0_2713,plain,
    ti(fun(X1,fun(X2,X1)),combk(X1,X2)) = combk(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_1753]) ).

cnf(c_0_2714,plain,
    ( ti(fun(X1,fun(X1,X1)),plus_plus(X1)) = plus_plus(X1)
    | ~ cancel_semigroup_add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1754]) ).

cnf(c_0_2715,plain,
    ( ti(fun(X1,fun(X1,X1)),plus_plus(X1)) = plus_plus(X1)
    | ~ ab_semigroup_add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1755]) ).

cnf(c_0_2716,plain,
    ( ti(fun(X1,fun(X1,X1)),plus_plus(X1)) = plus_plus(X1)
    | ~ monoid_add(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1756]) ).

cnf(c_0_2717,plain,
    ( ti(fun(X1,fun(X1,bool)),ord_less_eq(X1)) = ord_less_eq(X1)
    | ~ ord(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1757]) ).

cnf(c_0_2718,plain,
    ( ti(fun(X1,fun(X1,bool)),ord_less(X1)) = ord_less(X1)
    | ~ ord(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1758]) ).

cnf(c_0_2719,plain,
    ti(fun(X1,fun(X1,bool)),fequal(X1)) = fequal(X1),
    inference(split_conjunct,[status(thm)],[c_0_1759]) ).

cnf(c_0_2720,plain,
    ti(fun(fun(X1,bool),bool),finite_finite_1(X1)) = finite_finite_1(X1),
    inference(split_conjunct,[status(thm)],[c_0_1760]) ).

cnf(c_0_2721,plain,
    ti(fun(fun(X1,bool),nat),finite_card(X1)) = finite_card(X1),
    inference(split_conjunct,[status(thm)],[c_0_1761]) ).

cnf(c_0_2722,plain,
    ti(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),lba) = lba,
    inference(split_conjunct,[status(thm)],[c_0_1762]) ).

cnf(c_0_2723,plain,
    ti(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),lab) = lab,
    inference(split_conjunct,[status(thm)],[c_0_1763]) ).

cnf(c_0_2724,plain,
    ti(fun(bool,fun(bool,bool)),fdisj) = fdisj,
    inference(split_conjunct,[status(thm)],[c_0_1764]) ).

cnf(c_0_2725,plain,
    ti(fun(bool,fun(bool,bool)),fconj) = fconj,
    inference(split_conjunct,[status(thm)],[c_0_1765]) ).

cnf(c_0_2726,plain,
    ( ti(fun(X1,bool),ring_1_Ints(X1)) = ring_1_Ints(X1)
    | ~ ring_1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1766]) ).

cnf(c_0_2727,plain,
    ( ti(X1,X2) = zero_zero(X1)
    | ~ zero(X1)
    | zero_zero(X1) != ti(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1767]) ).

cnf(c_0_2728,plain,
    ( zero_zero(X1) = ti(X1,X2)
    | ~ zero(X1)
    | ti(X1,X2) != zero_zero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1767]) ).

cnf(c_0_2729,plain,
    ( ti(X1,X2) = one_one(X1)
    | ~ one(X1)
    | one_one(X1) != ti(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1768]) ).

cnf(c_0_2730,plain,
    ( one_one(X1) = ti(X1,X2)
    | ~ one(X1)
    | ti(X1,X2) != one_one(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1768]) ).

cnf(c_0_2731,plain,
    ti(X1,ti(X1,X2)) = ti(X1,X2),
    inference(split_conjunct,[status(thm)],[c_0_1769]) ).

cnf(c_0_2732,plain,
    ti(fun(X1,X1),combi(X1)) = combi(X1),
    inference(split_conjunct,[status(thm)],[c_0_1770]) ).

cnf(c_0_2733,plain,
    ( finite_finite(product_prod(X1,X2))
    | ~ finite_finite(X1)
    | ~ finite_finite(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1771]) ).

cnf(c_0_2734,plain,
    ( finite_finite(sum_sum(X1,X2))
    | ~ finite_finite(X1)
    | ~ finite_finite(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1772]) ).

cnf(c_0_2735,plain,
    ( finite_finite(fun(X1,X2))
    | ~ finite_finite(X1)
    | ~ finite_finite(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1773]) ).

cnf(c_0_2736,plain,
    ( ord(fun(X1,X2))
    | ~ ord(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1774]) ).

cnf(c_0_2737,plain,
    ( top(fun(X1,X2))
    | ~ top(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1775]) ).

cnf(c_0_2738,plain,
    ( order(fun(X1,X2))
    | ~ order(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1776]) ).

cnf(c_0_2739,plain,
    ( preorder(fun(X1,X2))
    | ~ preorder(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_1777]) ).

cnf(c_0_2740,plain,
    ti(fun(arrow_660593299e_indi,nat),h) = h,
    inference(split_conjunct,[status(thm)],[c_0_1778]) ).

cnf(c_0_2741,plain,
    ti(fun(bool,bool),fNot) = fNot,
    inference(split_conjunct,[status(thm)],[c_0_1779]) ).

cnf(c_0_2742,plain,
    ti(fun(nat,nat),suc) = suc,
    inference(split_conjunct,[status(thm)],[c_0_1780]) ).

cnf(c_0_2743,plain,
    ( ti(X1,top_top(X1)) = top_top(X1)
    | ~ top(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1781]) ).

cnf(c_0_2744,plain,
    ( ti(X1,zero_zero(X1)) = zero_zero(X1)
    | ~ zero(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1782]) ).

cnf(c_0_2745,plain,
    ( ti(X1,one_one(X1)) = one_one(X1)
    | ~ one(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1783]) ).

cnf(c_0_2746,plain,
    ( ti(bool,X1) = fFalse
    | ti(bool,X1) = fTrue ),
    inference(split_conjunct,[status(thm)],[c_0_1784]) ).

cnf(c_0_2747,plain,
    ( ti(bool,X1) = fFalse
    | ti(bool,X1) = fTrue ),
    inference(split_conjunct,[status(thm)],[c_0_1785]) ).

cnf(c_0_2748,plain,
    ti(X1,undefined(X1)) = undefined(X1),
    inference(split_conjunct,[status(thm)],[c_0_1786]) ).

cnf(c_0_2749,plain,
    ( one_one(X1) != zero_zero(X1)
    | ~ zero_neq_one(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1787]) ).

cnf(c_0_2750,plain,
    ( zero_zero(X1) != one_one(X1)
    | ~ zero_neq_one(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1788]) ).

cnf(c_0_2751,plain,
    ( finite_finite(option(X1))
    | ~ finite_finite(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_1789]) ).

cnf(c_0_2752,plain,
    ti(nat,n) = n,
    inference(split_conjunct,[status(thm)],[c_0_1790]) ).

cnf(c_0_2753,plain,
    ti(arrow_490897120le_alt,e) = e,
    inference(split_conjunct,[status(thm)],[c_0_1791]) ).

cnf(c_0_2754,plain,
    ti(arrow_490897120le_alt,b) = b,
    inference(split_conjunct,[status(thm)],[c_0_1792]) ).

cnf(c_0_2755,plain,
    ti(arrow_490897120le_alt,a) = a,
    inference(split_conjunct,[status(thm)],[c_0_1793]) ).

cnf(c_0_2756,plain,
    ti(bool,fTrue) = fTrue,
    inference(split_conjunct,[status(thm)],[c_0_1794]) ).

cnf(c_0_2757,plain,
    ti(bool,fFalse) = fFalse,
    inference(split_conjunct,[status(thm)],[c_0_1795]) ).

cnf(c_0_2758,plain,
    hBOOL(fTrue),
    inference(split_conjunct,[status(thm)],[c_0_1796]) ).

cnf(c_0_2759,plain,
    finite_finite(product_unit),
    inference(split_conjunct,[status(thm)],[c_0_1797]) ).

cnf(c_0_2760,plain,
    ord(bool),
    inference(split_conjunct,[status(thm)],[c_0_1798]) ).

cnf(c_0_2761,plain,
    top(bool),
    inference(split_conjunct,[status(thm)],[c_0_1799]) ).

cnf(c_0_2762,plain,
    order(bool),
    inference(split_conjunct,[status(thm)],[c_0_1800]) ).

cnf(c_0_2763,plain,
    finite_finite(bool),
    inference(split_conjunct,[status(thm)],[c_0_1801]) ).

cnf(c_0_2764,plain,
    preorder(bool),
    inference(split_conjunct,[status(thm)],[c_0_1802]) ).

cnf(c_0_2765,plain,
    one(nat),
    inference(split_conjunct,[status(thm)],[c_0_1803]) ).

cnf(c_0_2766,plain,
    zero(nat),
    inference(split_conjunct,[status(thm)],[c_0_1804]) ).

cnf(c_0_2767,plain,
    ord(nat),
    inference(split_conjunct,[status(thm)],[c_0_1805]) ).

cnf(c_0_2768,plain,
    order(nat),
    inference(split_conjunct,[status(thm)],[c_0_1806]) ).

cnf(c_0_2769,plain,
    monoid_add(nat),
    inference(split_conjunct,[status(thm)],[c_0_1807]) ).

cnf(c_0_2770,plain,
    linorder(nat),
    inference(split_conjunct,[status(thm)],[c_0_1808]) ).

cnf(c_0_2771,plain,
    preorder(nat),
    inference(split_conjunct,[status(thm)],[c_0_1809]) ).

cnf(c_0_2772,plain,
    zero_neq_one(nat),
    inference(split_conjunct,[status(thm)],[c_0_1810]) ).

cnf(c_0_2773,plain,
    comm_semiring_1(nat),
    inference(split_conjunct,[status(thm)],[c_0_1811]) ).

cnf(c_0_2774,plain,
    comm_monoid_add(nat),
    inference(split_conjunct,[status(thm)],[c_0_1812]) ).

cnf(c_0_2775,plain,
    ab_semigroup_add(nat),
    inference(split_conjunct,[status(thm)],[c_0_1813]) ).

cnf(c_0_2776,plain,
    linordered_semidom(nat),
    inference(split_conjunct,[status(thm)],[c_0_1814]) ).

cnf(c_0_2777,plain,
    cancel_semigroup_add(nat),
    inference(split_conjunct,[status(thm)],[c_0_1815]) ).

cnf(c_0_2778,plain,
    cancel146912293up_add(nat),
    inference(split_conjunct,[status(thm)],[c_0_1816]) ).

cnf(c_0_2779,plain,
    ordere216010020id_add(nat),
    inference(split_conjunct,[status(thm)],[c_0_1817]) ).

cnf(c_0_2780,plain,
    ordere779506340up_add(nat),
    inference(split_conjunct,[status(thm)],[c_0_1818]) ).

cnf(c_0_2781,plain,
    ordere236663937imp_le(nat),
    inference(split_conjunct,[status(thm)],[c_0_1819]) ).

cnf(c_0_2782,plain,
    ordere223160158up_add(nat),
    inference(split_conjunct,[status(thm)],[c_0_1820]) ).

cnf(c_0_2783,plain,
    semiri456707255roduct(nat),
    inference(split_conjunct,[status(thm)],[c_0_1821]) ).

cnf(c_0_2784,plain,
    a != b,
    inference(split_conjunct,[status(thm)],[c_0_1822]) ).

cnf(c_0_2785,plain,
    c != d,
    inference(split_conjunct,[status(thm)],[c_0_1823]) ).

cnf(c_0_2786,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))),lab)),lba))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))))) ),
    c_0_1824,
    [final] ).

cnf(c_0_2787,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),lab)),lba))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))))) ),
    c_0_1825,
    [final] ).

cnf(c_0_2788,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,p)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))))) ),
    c_0_1826,
    [final] ).

cnf(c_0_2789,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e))))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))),lab)),lba)))) ),
    c_0_1827,
    [final] ).

cnf(c_0_2790,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e))))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),lab)),lba)))) ),
    c_0_1828,
    [final] ).

cnf(c_0_2791,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e))))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,p))) ),
    c_0_1829,
    [final] ).

cnf(c_0_2792,plain,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))))),
    c_0_1830,
    [final] ).

cnf(c_0_2793,plain,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))))),
    c_0_1831,
    [final] ).

cnf(c_0_2794,plain,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))))),
    c_0_1832,
    [final] ).

cnf(c_0_2795,plain,
    hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))),arrow_1111136790e_Prof)),
    c_0_1833,
    [final] ).

cnf(c_0_2796,plain,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),esk28_0),one_one(nat))))),lab)),lba)))),
    c_0_1834,
    [final] ).

cnf(c_0_2797,plain,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),esk27_0),one_one(nat))))),lab)),lba)))),
    c_0_1835,
    [final] ).

cnf(c_0_2798,plain,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))),lab)),lba)))),
    c_0_1836,
    [final] ).

cnf(c_0_2799,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),X1))),lab)),lba))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),esk28_0)) ),
    c_0_1837,
    [final] ).

cnf(c_0_2800,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),X1))),lab)),lba))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),esk27_0)) ),
    c_0_1838,
    [final] ).

cnf(c_0_2801,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),X1))),lab)),lba))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),n)) ),
    c_0_1839,
    [final] ).

cnf(c_0_2802,plain,
    hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),X1))),lab)),lba)),arrow_1111136790e_Prof)),
    c_0_1840,
    [final] ).

cnf(c_0_2803,plain,
    ( hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(fun(product_prod(X1,X2),bool),fun(fun(product_prod(X1,X2),bool),bool),ord_less_eq(fun(product_prod(X1,X2),bool)),X3),X4))
    | ~ hBOOL(hAPP(fun(X1,fun(X2,bool)),bool,hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,fun(X2,bool)),bool),ord_less_eq(fun(X1,fun(X2,bool))),hAPP(fun(product_prod(X1,X2),bool),fun(X1,fun(X2,bool)),hAPP(fun(X1,fun(fun(product_prod(X1,X2),bool),fun(X2,bool))),fun(fun(product_prod(X1,X2),bool),fun(X1,fun(X2,bool))),combc(X1,fun(product_prod(X1,X2),bool),fun(X2,bool)),hAPP(fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),fun(X1,fun(fun(product_prod(X1,X2),bool),fun(X2,bool))),hAPP(fun(fun(X2,fun(fun(product_prod(X1,X2),bool),bool)),fun(fun(product_prod(X1,X2),bool),fun(X2,bool))),fun(fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),fun(X1,fun(fun(product_prod(X1,X2),bool),fun(X2,bool)))),combb(fun(X2,fun(fun(product_prod(X1,X2),bool),bool)),fun(fun(product_prod(X1,X2),bool),fun(X2,bool)),X1),combc(X2,fun(product_prod(X1,X2),bool),bool)),hAPP(fun(X1,fun(X2,product_prod(X1,X2))),fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),hAPP(fun(fun(X2,product_prod(X1,X2)),fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),fun(fun(X1,fun(X2,product_prod(X1,X2))),fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool)))),combb(fun(X2,product_prod(X1,X2)),fun(X2,fun(fun(product_prod(X1,X2),bool),bool)),X1),hAPP(fun(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool)),fun(fun(X2,product_prod(X1,X2)),fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),combb(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),X2),member(product_prod(X1,X2)))),product_Pair(X1,X2)))),X3)),hAPP(fun(product_prod(X1,X2),bool),fun(X1,fun(X2,bool)),hAPP(fun(X1,fun(fun(product_prod(X1,X2),bool),fun(X2,bool))),fun(fun(product_prod(X1,X2),bool),fun(X1,fun(X2,bool))),combc(X1,fun(product_prod(X1,X2),bool),fun(X2,bool)),hAPP(fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),fun(X1,fun(fun(product_prod(X1,X2),bool),fun(X2,bool))),hAPP(fun(fun(X2,fun(fun(product_prod(X1,X2),bool),bool)),fun(fun(product_prod(X1,X2),bool),fun(X2,bool))),fun(fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),fun(X1,fun(fun(product_prod(X1,X2),bool),fun(X2,bool)))),combb(fun(X2,fun(fun(product_prod(X1,X2),bool),bool)),fun(fun(product_prod(X1,X2),bool),fun(X2,bool)),X1),combc(X2,fun(product_prod(X1,X2),bool),bool)),hAPP(fun(X1,fun(X2,product_prod(X1,X2))),fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),hAPP(fun(fun(X2,product_prod(X1,X2)),fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),fun(fun(X1,fun(X2,product_prod(X1,X2))),fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool)))),combb(fun(X2,product_prod(X1,X2)),fun(X2,fun(fun(product_prod(X1,X2),bool),bool)),X1),hAPP(fun(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool)),fun(fun(X2,product_prod(X1,X2)),fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),combb(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),X2),member(product_prod(X1,X2)))),product_Pair(X1,X2)))),X4))) ),
    c_0_1841,
    [final] ).

cnf(c_0_2804,plain,
    ( hBOOL(hAPP(fun(X1,fun(X2,bool)),bool,hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,fun(X2,bool)),bool),ord_less_eq(fun(X1,fun(X2,bool))),hAPP(fun(product_prod(X1,X2),bool),fun(X1,fun(X2,bool)),hAPP(fun(X1,fun(fun(product_prod(X1,X2),bool),fun(X2,bool))),fun(fun(product_prod(X1,X2),bool),fun(X1,fun(X2,bool))),combc(X1,fun(product_prod(X1,X2),bool),fun(X2,bool)),hAPP(fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),fun(X1,fun(fun(product_prod(X1,X2),bool),fun(X2,bool))),hAPP(fun(fun(X2,fun(fun(product_prod(X1,X2),bool),bool)),fun(fun(product_prod(X1,X2),bool),fun(X2,bool))),fun(fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),fun(X1,fun(fun(product_prod(X1,X2),bool),fun(X2,bool)))),combb(fun(X2,fun(fun(product_prod(X1,X2),bool),bool)),fun(fun(product_prod(X1,X2),bool),fun(X2,bool)),X1),combc(X2,fun(product_prod(X1,X2),bool),bool)),hAPP(fun(X1,fun(X2,product_prod(X1,X2))),fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),hAPP(fun(fun(X2,product_prod(X1,X2)),fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),fun(fun(X1,fun(X2,product_prod(X1,X2))),fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool)))),combb(fun(X2,product_prod(X1,X2)),fun(X2,fun(fun(product_prod(X1,X2),bool),bool)),X1),hAPP(fun(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool)),fun(fun(X2,product_prod(X1,X2)),fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),combb(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),X2),member(product_prod(X1,X2)))),product_Pair(X1,X2)))),X3)),hAPP(fun(product_prod(X1,X2),bool),fun(X1,fun(X2,bool)),hAPP(fun(X1,fun(fun(product_prod(X1,X2),bool),fun(X2,bool))),fun(fun(product_prod(X1,X2),bool),fun(X1,fun(X2,bool))),combc(X1,fun(product_prod(X1,X2),bool),fun(X2,bool)),hAPP(fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),fun(X1,fun(fun(product_prod(X1,X2),bool),fun(X2,bool))),hAPP(fun(fun(X2,fun(fun(product_prod(X1,X2),bool),bool)),fun(fun(product_prod(X1,X2),bool),fun(X2,bool))),fun(fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),fun(X1,fun(fun(product_prod(X1,X2),bool),fun(X2,bool)))),combb(fun(X2,fun(fun(product_prod(X1,X2),bool),bool)),fun(fun(product_prod(X1,X2),bool),fun(X2,bool)),X1),combc(X2,fun(product_prod(X1,X2),bool),bool)),hAPP(fun(X1,fun(X2,product_prod(X1,X2))),fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),hAPP(fun(fun(X2,product_prod(X1,X2)),fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),fun(fun(X1,fun(X2,product_prod(X1,X2))),fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool)))),combb(fun(X2,product_prod(X1,X2)),fun(X2,fun(fun(product_prod(X1,X2),bool),bool)),X1),hAPP(fun(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool)),fun(fun(X2,product_prod(X1,X2)),fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),combb(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),X2),member(product_prod(X1,X2)))),product_Pair(X1,X2)))),X4)))
    | ~ hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(fun(product_prod(X1,X2),bool),fun(fun(product_prod(X1,X2),bool),bool),ord_less_eq(fun(product_prod(X1,X2),bool)),X3),X4)) ),
    c_0_1842,
    [final] ).

cnf(c_0_2805,plain,
    ( hAPP(nat,nat,suc,hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),hAPP(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool)),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool))),combb(nat,fun(fun(nat,bool),bool),nat),member(nat)),suc)),X1))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X2))))) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),X1))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,X2)))))
    | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),X1)) ),
    c_0_1843,
    [final] ).

cnf(c_0_2806,plain,
    ( hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),hAPP(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool)),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool))),combb(nat,fun(fun(nat,bool),bool),nat),member(nat)),suc)),X1))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X2)))) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),X1))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,X2)))))
    | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),X1)) ),
    c_0_1844,
    [final] ).

cnf(c_0_2807,plain,
    ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6))
    | ~ order(X1)
    | ~ order(X2)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X5,X4)),X6))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,esk58_6(X1,X2,X5,X6,X3,X4))),hAPP(X1,X2,X5,esk59_6(X1,X2,X5,X6,X3,X4)))) ),
    c_0_1845,
    [final] ).

cnf(c_0_2808,plain,
    ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6))
    | ~ order(X1)
    | ~ order(X2)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X4)),X6))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X5,esk48_6(X1,X2,X5,X6,X3,X4))),hAPP(X1,X2,X5,esk49_6(X1,X2,X5,X6,X3,X4)))) ),
    c_0_1846,
    [final] ).

cnf(c_0_2809,plain,
    ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5))
    | ~ order(X1)
    | ~ order(X2)
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X4)),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X4))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,esk43_6(X1,X2,X6,X3,X4,X5))),hAPP(X1,X2,X3,esk42_6(X1,X2,X6,X3,X4,X5)))) ),
    c_0_1847,
    [final] ).

cnf(c_0_2810,plain,
    ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5))
    | ~ ord(X1)
    | ~ order(X2)
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,X4)),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X4))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,esk41_6(X1,X2,X6,X3,X4,X5))),hAPP(X1,X2,X3,esk40_6(X1,X2,X6,X3,X4,X5)))) ),
    c_0_1848,
    [final] ).

cnf(c_0_2811,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4)))
    | ~ order(X1)
    | ~ order(X2)
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X3),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X3)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X6,esk57_6(X1,X2,X5,X6,X3,X4))),hAPP(X2,X1,X6,esk56_6(X1,X2,X5,X6,X3,X4)))) ),
    c_0_1849,
    [final] ).

cnf(c_0_2812,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4)))
    | ~ order(X1)
    | ~ order(X2)
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X3),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),hAPP(X2,X1,X6,X3)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X6,esk55_6(X1,X2,X5,X6,X3,X4))),hAPP(X2,X1,X6,esk54_6(X1,X2,X5,X6,X3,X4)))) ),
    c_0_1850,
    [final] ).

cnf(c_0_2813,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6)))
    | ~ order(X1)
    | ~ order(X2)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X5)))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X5),X6))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X4,esk46_6(X1,X2,X6,X3,X4,X5))),hAPP(X2,X1,X4,esk47_6(X1,X2,X6,X3,X4,X5)))) ),
    c_0_1851,
    [final] ).

cnf(c_0_2814,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6)))
    | ~ order(X1)
    | ~ order(X2)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),hAPP(X2,X1,X4,X5)))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X5),X6))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X4,esk44_6(X1,X2,X6,X3,X4,X5))),hAPP(X2,X1,X4,esk45_6(X1,X2,X6,X3,X4,X5)))) ),
    c_0_1852,
    [final] ).

cnf(c_0_2815,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,esk2_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,esk2_6(X6,X5,X3,X4,X1,X2)))) ),
    c_0_1853,
    [final] ).

cnf(c_0_2816,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,esk1_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,esk1_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    c_0_1854,
    [final] ).

cnf(c_0_2817,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,esk1_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,esk1_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6))) ),
    c_0_1855,
    [final] ).

cnf(c_0_2818,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,esk4_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,esk4_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    c_0_1856,
    [final] ).

cnf(c_0_2819,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,esk4_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,esk4_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6))) ),
    c_0_1857,
    [final] ).

cnf(c_0_2820,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,esk2_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,esk2_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    c_0_1858,
    [final] ).

cnf(c_0_2821,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,esk1_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,esk1_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    c_0_1859,
    [final] ).

cnf(c_0_2822,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,esk1_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,esk1_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6))) ),
    c_0_1860,
    [final] ).

cnf(c_0_2823,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,esk4_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,esk4_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    c_0_1861,
    [final] ).

cnf(c_0_2824,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,esk4_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,esk4_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6))) ),
    c_0_1862,
    [final] ).

cnf(c_0_2825,plain,
    ( hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),X1))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,X2))))) != zero_zero(nat)
    | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),X1)) ),
    c_0_1863,
    [final] ).

cnf(c_0_2826,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    c_0_1864,
    [final] ).

cnf(c_0_2827,plain,
    ( hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,X1),X2))
    | ~ hBOOL(hAPP(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1111136790e_Prof),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_2064824852le_Lin))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),esk24_2(X2,X1)),esk25_2(X2,X1))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,esk23_2(X2,X1)))) ),
    c_0_1865,
    [final] ).

cnf(c_0_2828,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    c_0_1866,
    [final] ).

cnf(c_0_2829,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    c_0_1867,
    [final] ).

cnf(c_0_2830,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    c_0_1868,
    [final] ).

cnf(c_0_2831,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    c_0_1869,
    [final] ).

cnf(c_0_2832,plain,
    ( hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,X1),X2))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),esk24_2(X2,X1)),esk25_2(X2,X1))),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),esk23_2(X2,X1),X2)))
    | ~ hBOOL(hAPP(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1111136790e_Prof),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_2064824852le_Lin)))) ),
    c_0_1870,
    [final] ).

cnf(c_0_2833,plain,
    ( hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,X1),X2))
    | hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),esk23_2(X2,X1)),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1111136790e_Prof),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_2064824852le_Lin)))) ),
    c_0_1871,
    [final] ).

cnf(c_0_2834,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X3)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X2),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,esk9_5(X1,X2,X3,X4,X5))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X2,esk9_5(X1,X2,X3,X4,X5))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X2))) ),
    c_0_1872,
    [final] ).

cnf(c_0_2835,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X2)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X2),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,esk9_5(X1,X2,X3,X4,X5))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X2,esk9_5(X1,X2,X3,X4,X5))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X3))) ),
    c_0_1873,
    [final] ).

cnf(c_0_2836,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,esk3_5(X5,X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,esk3_5(X5,X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4))) ),
    c_0_1874,
    [final] ).

cnf(c_0_2837,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,esk3_5(X5,X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,esk3_5(X5,X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    c_0_1875,
    [final] ).

cnf(c_0_2838,plain,
    ( hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,X1),X2))
    | ~ hBOOL(hAPP(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1111136790e_Prof),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_2064824852le_Lin))))
    | ti(arrow_490897120le_alt,esk25_2(X2,X1)) != ti(arrow_490897120le_alt,esk24_2(X2,X1)) ),
    c_0_1876,
    [final] ).

cnf(c_0_2839,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    c_0_1877,
    [final] ).

cnf(c_0_2840,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    c_0_1878,
    [final] ).

cnf(c_0_2841,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fdisj),X2)),X3)))) ),
    c_0_1879,
    [final] ).

cnf(c_0_2842,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X3)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fdisj),X2)),X3)))) ),
    c_0_1880,
    [final] ).

cnf(c_0_2843,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    c_0_1881,
    [final] ).

cnf(c_0_2844,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    c_0_1882,
    [final] ).

cnf(c_0_2845,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    c_0_1883,
    [final] ).

cnf(c_0_2846,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    c_0_1884,
    [final] ).

cnf(c_0_2847,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    c_0_1885,
    [final] ).

cnf(c_0_2848,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    c_0_1886,
    [final] ).

cnf(c_0_2849,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    c_0_1887,
    [final] ).

cnf(c_0_2850,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    c_0_1888,
    [final] ).

cnf(c_0_2851,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,esk9_5(X1,X2,X3,X4,X5))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X2,esk9_5(X1,X2,X3,X4,X5))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X3)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X2),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X2))) ),
    c_0_1889,
    [final] ).

cnf(c_0_2852,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,esk9_5(X1,X2,X3,X4,X5))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X2,esk9_5(X1,X2,X3,X4,X5))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X2)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X2),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X3))) ),
    c_0_1890,
    [final] ).

cnf(c_0_2853,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,esk3_5(X5,X4,X3,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,esk3_5(X5,X4,X3,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4))) ),
    c_0_1891,
    [final] ).

cnf(c_0_2854,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,esk3_5(X5,X4,X3,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,esk3_5(X5,X4,X3,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    c_0_1892,
    [final] ).

cnf(c_0_2855,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,esk5_4(X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,esk5_4(X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3))) ),
    c_0_1893,
    [final] ).

cnf(c_0_2856,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,esk5_4(X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,esk5_4(X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4))) ),
    c_0_1894,
    [final] ).

cnf(c_0_2857,plain,
    ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),esk58_6(X1,X2,X5,X6,X3,X4)),esk59_6(X1,X2,X5,X6,X3,X4)))
    | ~ order(X1)
    | ~ order(X2)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X5,X4)),X6)) ),
    c_0_1895,
    [final] ).

cnf(c_0_2858,plain,
    ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),esk48_6(X1,X2,X5,X6,X3,X4)),esk49_6(X1,X2,X5,X6,X3,X4)))
    | ~ order(X1)
    | ~ order(X2)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X4)),X6)) ),
    c_0_1896,
    [final] ).

cnf(c_0_2859,plain,
    ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),esk43_6(X1,X2,X6,X3,X4,X5)),esk42_6(X1,X2,X6,X3,X4,X5)))
    | ~ order(X1)
    | ~ order(X2)
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X4)),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X4)) ),
    c_0_1897,
    [final] ).

cnf(c_0_2860,plain,
    ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),esk41_6(X1,X2,X6,X3,X4,X5)),esk40_6(X1,X2,X6,X3,X4,X5)))
    | ~ ord(X1)
    | ~ order(X2)
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,X4)),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X4)) ),
    c_0_1898,
    [final] ).

cnf(c_0_2861,plain,
    hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),X1)),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X2))))),
    c_0_1899,
    [final] ).

cnf(c_0_2862,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4)))
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),esk57_6(X1,X2,X5,X6,X3,X4)),esk56_6(X1,X2,X5,X6,X3,X4)))
    | ~ order(X1)
    | ~ order(X2)
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X3),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X3))) ),
    c_0_1900,
    [final] ).

cnf(c_0_2863,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4)))
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),esk55_6(X1,X2,X5,X6,X3,X4)),esk54_6(X1,X2,X5,X6,X3,X4)))
    | ~ order(X1)
    | ~ order(X2)
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X3),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),hAPP(X2,X1,X6,X3))) ),
    c_0_1901,
    [final] ).

cnf(c_0_2864,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6)))
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),esk46_6(X1,X2,X6,X3,X4,X5)),esk47_6(X1,X2,X6,X3,X4,X5)))
    | ~ order(X1)
    | ~ order(X2)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X5)))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X5),X6)) ),
    c_0_1902,
    [final] ).

cnf(c_0_2865,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6)))
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),esk44_6(X1,X2,X6,X3,X4,X5)),esk45_6(X1,X2,X6,X3,X4,X5)))
    | ~ order(X1)
    | ~ order(X2)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),hAPP(X2,X1,X4,X5)))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X5),X6)) ),
    c_0_1903,
    [final] ).

cnf(c_0_2866,plain,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    c_0_1904,
    [final] ).

cnf(c_0_2867,plain,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    c_0_1905,
    [final] ).

cnf(c_0_2868,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    c_0_1906,
    [final] ).

cnf(c_0_2869,plain,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    c_0_1907,
    [final] ).

cnf(c_0_2870,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,esk5_4(X4,X3,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,esk5_4(X4,X3,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3))) ),
    c_0_1908,
    [final] ).

cnf(c_0_2871,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,esk5_4(X4,X3,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,esk5_4(X4,X3,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4))) ),
    c_0_1909,
    [final] ).

cnf(c_0_2872,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X5)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    c_0_1910,
    [final] ).

cnf(c_0_2873,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X1)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    c_0_1911,
    [final] ).

cnf(c_0_2874,plain,
    ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(fun(X1,X2),bool),fun(fun(fun(X1,X2),bool),bool),ord_less_eq(fun(fun(X1,X2),bool)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X3),X4)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X3),X5)))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),hAPP(X1,fun(X2,bool),X4,esk52_5(X2,X1,X4,X5,X3))),hAPP(X1,fun(X2,bool),X5,esk52_5(X2,X1,X4,X5,X3)))) ),
    c_0_1912,
    [final] ).

cnf(c_0_2875,plain,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    c_0_1913,
    [final] ).

cnf(c_0_2876,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    c_0_1914,
    [final] ).

cnf(c_0_2877,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk67_6(X2,X1,X3,X4,X5,X6)),X6))
    | hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X5),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X6),X3)))
    | ~ hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X4),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X6),X3))) ),
    c_0_1915,
    [final] ).

cnf(c_0_2878,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk67_6(X2,X1,X3,X4,X5,X6)),X6))
    | hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X4),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X6),X3)))
    | ~ hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X5),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X6),X3))) ),
    c_0_1916,
    [final] ).

cnf(c_0_2879,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    c_0_1917,
    [final] ).

cnf(c_0_2880,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    c_0_1918,
    [final] ).

cnf(c_0_2881,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fdisj),X2)),X3))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X3)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2))) ),
    c_0_1919,
    [final] ).

cnf(c_0_2882,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    c_0_1920,
    [final] ).

cnf(c_0_2883,plain,
    ( ti(fun(product_prod(X1,X2),bool),X3) = ti(fun(product_prod(X1,X2),bool),X4)
    | ~ hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),member(product_prod(X1,X2)),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),esk21_4(X1,X2,X4,X3)),esk22_4(X1,X2,X4,X3))),X4))
    | ~ hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),member(product_prod(X1,X2)),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),esk21_4(X1,X2,X4,X3)),esk22_4(X1,X2,X4,X3))),X3)) ),
    c_0_1921,
    [final] ).

cnf(c_0_2884,plain,
    hBOOL(hAPP(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),f),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1111136790e_Prof),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_2064824852le_Lin)))),
    c_0_1922,
    [final] ).

cnf(c_0_2885,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    c_0_1923,
    [final] ).

cnf(c_0_2886,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    c_0_1924,
    [final] ).

cnf(c_0_2887,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    c_0_1925,
    [final] ).

cnf(c_0_2888,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X2)),X3))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2))) ),
    c_0_1926,
    [final] ).

cnf(c_0_2889,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X2)),X3))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X3))) ),
    c_0_1927,
    [final] ).

cnf(c_0_2890,plain,
    ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less_eq(nat)),X1)),X2))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),esk77_2(X2,X1)),hAPP(nat,nat,X1,esk77_2(X2,X1)))) ),
    c_0_1928,
    [final] ).

cnf(c_0_2891,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    c_0_1929,
    [final] ).

cnf(c_0_2892,plain,
    ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X3),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X4),X5)))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X3,esk68_5(X2,X1,X3,X5,X4))),hAPP(X1,fun(X2,bool),X5,esk68_5(X2,X1,X3,X5,X4)))) ),
    c_0_1930,
    [final] ).

cnf(c_0_2893,plain,
    ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X3),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X4),X5)))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X3,esk33_5(X2,X1,X3,X5,X4))),hAPP(X1,fun(X2,bool),X5,esk33_5(X2,X1,X3,X5,X4)))) ),
    c_0_1931,
    [final] ).

cnf(c_0_2894,plain,
    ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X5),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X6),X4)))
    | hAPP(X1,X2,X3,esk67_6(X2,X1,X4,X3,X5,X6)) != hAPP(X1,X2,X5,esk67_6(X2,X1,X4,X3,X5,X6))
    | ~ hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X3),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X6),X4))) ),
    c_0_1932,
    [final] ).

cnf(c_0_2895,plain,
    ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X3),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X6),X4)))
    | hAPP(X1,X2,X3,esk67_6(X2,X1,X4,X3,X5,X6)) != hAPP(X1,X2,X5,esk67_6(X2,X1,X4,X3,X5,X6))
    | ~ hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X5),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X6),X4))) ),
    c_0_1933,
    [final] ).

cnf(c_0_2896,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    c_0_1934,
    [final] ).

cnf(c_0_2897,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X5)),X3))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1) ),
    c_0_1935,
    [final] ).

cnf(c_0_2898,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    c_0_1936,
    [final] ).

cnf(c_0_2899,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X1)),X3))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2) ),
    c_0_1937,
    [final] ).

cnf(c_0_2900,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X5)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    c_0_1938,
    [final] ).

cnf(c_0_2901,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    c_0_1939,
    [final] ).

cnf(c_0_2902,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X1)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    c_0_1940,
    [final] ).

cnf(c_0_2903,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    c_0_1941,
    [final] ).

cnf(c_0_2904,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    c_0_1942,
    [final] ).

cnf(c_0_2905,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    c_0_1943,
    [final] ).

cnf(c_0_2906,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
    | ~ linordered_idom(X1)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),ring_1_Ints(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),one_one(X1)),X2)),X2)),zero_zero(X1))) ),
    c_0_1944,
    [final] ).

cnf(c_0_2907,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    c_0_1945,
    [final] ).

cnf(c_0_2908,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    c_0_1946,
    [final] ).

cnf(c_0_2909,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    c_0_1947,
    [final] ).

cnf(c_0_2910,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    c_0_1948,
    [final] ).

cnf(c_0_2911,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    c_0_1949,
    [final] ).

cnf(c_0_2912,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    c_0_1950,
    [final] ).

cnf(c_0_2913,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    c_0_1951,
    [final] ).

cnf(c_0_2914,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba)) ),
    c_0_1952,
    [final] ).

cnf(c_0_2915,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba)) ),
    c_0_1953,
    [final] ).

cnf(c_0_2916,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X5)),X3))
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1) ),
    c_0_1954,
    [final] ).

cnf(c_0_2917,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X1)),X3))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2) ),
    c_0_1955,
    [final] ).

cnf(c_0_2918,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2))) ),
    c_0_1956,
    [final] ).

cnf(c_0_2919,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3))
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2))) ),
    c_0_1957,
    [final] ).

cnf(c_0_2920,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X1) ),
    c_0_1958,
    [final] ).

cnf(c_0_2921,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X2) ),
    c_0_1959,
    [final] ).

cnf(c_0_2922,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    c_0_1960,
    [final] ).

cnf(c_0_2923,plain,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    c_0_1961,
    [final] ).

cnf(c_0_2924,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    c_0_1962,
    [final] ).

cnf(c_0_2925,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    c_0_1963,
    [final] ).

cnf(c_0_2926,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    c_0_1964,
    [final] ).

cnf(c_0_2927,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    c_0_1965,
    [final] ).

cnf(c_0_2928,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    c_0_1966,
    [final] ).

cnf(c_0_2929,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    c_0_1967,
    [final] ).

cnf(c_0_2930,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),X2,hAPP(fun(X3,bool),X1,X4,X5)),hAPP(fun(X3,bool),X1,X4,X6)) = hAPP(fun(X3,bool),X1,X4,X6)
    | ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X5),X6))
    | ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X6))
    | ~ hBOOL(hAPP(fun(fun(X3,bool),X1),bool,hAPP(fun(X3,X1),fun(fun(fun(X3,bool),X1),bool),hAPP(X1,fun(fun(X3,X1),fun(fun(fun(X3,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X3,X1),fun(fun(fun(X3,bool),X1),bool))),finite908156982e_idem(X1,X3),X2),X7),X8),X4)) ),
    c_0_1968,
    [final] ).

cnf(c_0_2931,plain,
    ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X3),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X4),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),X5))))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X3,esk65_5(X2,X1,X3,X5,X4))),X5)) ),
    c_0_1969,
    [final] ).

cnf(c_0_2932,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),X2,hAPP(X3,X1,X4,X5)),hAPP(fun(X3,bool),X1,X6,X7)) = hAPP(fun(X3,bool),X1,X6,X7)
    | ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X5),X7))
    | ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X7))
    | ~ hBOOL(hAPP(fun(fun(X3,bool),X1),bool,hAPP(fun(X3,X1),fun(fun(fun(X3,bool),X1),bool),hAPP(X1,fun(fun(X3,X1),fun(fun(fun(X3,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X3,X1),fun(fun(fun(X3,bool),X1),bool))),finite908156982e_idem(X1,X3),X2),X8),X4),X6)) ),
    c_0_1970,
    [final] ).

cnf(c_0_2933,plain,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    c_0_1971,
    [final] ).

cnf(c_0_2934,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    c_0_1972,
    [final] ).

cnf(c_0_2935,plain,
    ( hAPP(fun(X1,bool),nat,finite_card(X1),X2) = hAPP(fun(X3,bool),nat,finite_card(X3),X4)
    | ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X5),X4))
    | ~ hBOOL(hAPP(fun(fun(X3,X1),bool),bool,hAPP(fun(X3,X1),fun(fun(fun(X3,X1),bool),bool),member(fun(X3,X1)),X5),hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool)),pi(X3,X1),X4),hAPP(fun(X1,bool),fun(X3,fun(X1,bool)),combk(fun(X1,bool),X3),X2))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X6),X2))
    | ~ hBOOL(hAPP(fun(fun(X1,X3),bool),bool,hAPP(fun(X1,X3),fun(fun(fun(X1,X3),bool),bool),member(fun(X1,X3)),X6),hAPP(fun(X1,fun(X3,bool)),fun(fun(X1,X3),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X3,bool)),fun(fun(X1,X3),bool)),pi(X1,X3),X2),hAPP(fun(X3,bool),fun(X1,fun(X3,bool)),combk(fun(X3,bool),X1),X4)))) ),
    c_0_1973,
    [final] ).

cnf(c_0_2936,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    c_0_1974,
    [final] ).

cnf(c_0_2937,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    c_0_1975,
    [final] ).

cnf(c_0_2938,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    c_0_1976,
    [final] ).

cnf(c_0_2939,plain,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    c_0_1977,
    [final] ).

cnf(c_0_2940,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    c_0_1978,
    [final] ).

cnf(c_0_2941,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1) ),
    c_0_1979,
    [final] ).

cnf(c_0_2942,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2) ),
    c_0_1980,
    [final] ).

cnf(c_0_2943,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    c_0_1981,
    [final] ).

cnf(c_0_2944,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X5)),X3))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1) ),
    c_0_1982,
    [final] ).

cnf(c_0_2945,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1) ),
    c_0_1983,
    [final] ).

cnf(c_0_2946,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    c_0_1984,
    [final] ).

cnf(c_0_2947,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X1)),X3))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2) ),
    c_0_1985,
    [final] ).

cnf(c_0_2948,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2) ),
    c_0_1986,
    [final] ).

cnf(c_0_2949,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    c_0_1987,
    [final] ).

cnf(c_0_2950,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    c_0_1988,
    [final] ).

cnf(c_0_2951,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X1) ),
    c_0_1989,
    [final] ).

cnf(c_0_2952,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X2) ),
    c_0_1990,
    [final] ).

cnf(c_0_2953,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    c_0_1991,
    [final] ).

cnf(c_0_2954,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba)) ),
    c_0_1992,
    [final] ).

cnf(c_0_2955,plain,
    ( ti(fun(product_prod(X1,X2),bool),X3) = ti(fun(product_prod(X1,X2),bool),X4)
    | hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),member(product_prod(X1,X2)),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),esk21_4(X1,X2,X4,X3)),esk22_4(X1,X2,X4,X3))),X4))
    | hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),member(product_prod(X1,X2)),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),esk21_4(X1,X2,X4,X3)),esk22_4(X1,X2,X4,X3))),X3)) ),
    c_0_1993,
    [final] ).

cnf(c_0_2956,plain,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    c_0_1994,
    [final] ).

cnf(c_0_2957,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,X4)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,esk14_4(X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,X3)) ),
    c_0_1995,
    [final] ).

cnf(c_0_2958,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    c_0_1996,
    [final] ).

cnf(c_0_2959,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X5) ),
    c_0_1997,
    [final] ).

cnf(c_0_2960,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X5) ),
    c_0_1998,
    [final] ).

cnf(c_0_2961,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    c_0_1999,
    [final] ).

cnf(c_0_2962,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),X2,X3),X3) = ti(X1,X3)
    | ~ hBOOL(hAPP(fun(fun(X4,bool),X1),bool,hAPP(fun(X4,X1),fun(fun(fun(X4,bool),X1),bool),hAPP(X1,fun(fun(X4,X1),fun(fun(fun(X4,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X4,X1),fun(fun(fun(X4,bool),X1),bool))),finite908156982e_idem(X1,X4),X2),X5),X6),X7)) ),
    c_0_2000,
    [final] ).

cnf(c_0_2963,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    c_0_2001,
    [final] ).

cnf(c_0_2964,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    c_0_2002,
    [final] ).

cnf(c_0_2965,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba)) ),
    c_0_2003,
    [final] ).

cnf(c_0_2966,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    c_0_2004,
    [final] ).

cnf(c_0_2967,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1))) ),
    c_0_2005,
    [final] ).

cnf(c_0_2968,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    c_0_2006,
    [final] ).

cnf(c_0_2969,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),one_one(X1)),X2)),X2)),zero_zero(X1)))
    | ~ linordered_idom(X1)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),ring_1_Ints(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1))) ),
    c_0_2007,
    [final] ).

cnf(c_0_2970,plain,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X2,bool),nat,finite_card(X2),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X4))),hAPP(fun(X1,bool),nat,finite_card(X1),X4))) ),
    c_0_2008,
    [final] ).

cnf(c_0_2971,plain,
    ( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X1),X2),X3)),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X1),arrow_2064824852le_Lin)) ),
    c_0_2009,
    [final] ).

cnf(c_0_2972,plain,
    ( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X1),X2),X3)),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X1),arrow_2064824852le_Lin)) ),
    c_0_2010,
    [final] ).

cnf(c_0_2973,plain,
    ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),esk12_1(X1)),esk13_1(X1))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,esk11_1(X1))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),esk12_1(X1)),esk13_1(X1))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,esk10_1(X1)))) ),
    c_0_2011,
    [final] ).

cnf(c_0_2974,plain,
    ( ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X1),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),X1))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X2)),X1)) ),
    c_0_2012,
    [final] ).

cnf(c_0_2975,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin)) ),
    c_0_2013,
    [final] ).

cnf(c_0_2976,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(X1,bool)),combc(X1,fun(X1,bool),bool),member(X1)),X2)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(X1,bool)),combc(X1,fun(X1,bool),bool),member(X1)),X3))) ),
    c_0_2014,
    [final] ).

cnf(c_0_2977,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),hAPP(fun(X2,X3),fun(X2,X1),hAPP(fun(X3,X1),fun(fun(X2,X3),fun(X2,X1)),combb(X3,X1,X2),X4),X5)),top_top(fun(X2,bool)))))
    | ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),hAPP(fun(X2,bool),fun(X3,bool),hAPP(fun(X2,X3),fun(fun(X2,bool),fun(X3,bool)),image(X2,X3),X5),top_top(fun(X2,bool))))) ),
    c_0_2015,
    [final] ).

cnf(c_0_2978,plain,
    ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(fun(X1,X2),bool),fun(fun(fun(X1,X2),bool),bool),ord_less_eq(fun(fun(X1,X2),bool)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X3),X4)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X3),X5)))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk52_5(X2,X1,X4,X5,X3)),X3)) ),
    c_0_2016,
    [final] ).

cnf(c_0_2979,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    c_0_2017,
    [final] ).

cnf(c_0_2980,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X4)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X3),X4))) ),
    c_0_2018,
    [final] ).

cnf(c_0_2981,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X3),X4))) ),
    c_0_2019,
    [final] ).

cnf(c_0_2982,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    c_0_2020,
    [final] ).

cnf(c_0_2983,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X2,X1,hAPP(fun(X1,X2),fun(X2,X1),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)),hilbert_inv_into(X1,X2),X3),X4),X5)),X3))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X5),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X4),X3))) ),
    c_0_2021,
    [final] ).

cnf(c_0_2984,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,X1,X2)),X3)),hAPP(nat,nat,X1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,X1,esk61_3(X2,X3,X1))),hAPP(nat,nat,X1,esk62_3(X2,X3,X1)))) ),
    c_0_2022,
    [final] ).

cnf(c_0_2985,plain,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,hAPP(nat,arrow_660593299e_indi,hAPP(fun(arrow_660593299e_indi,nat),fun(nat,arrow_660593299e_indi),hAPP(fun(arrow_660593299e_indi,bool),fun(fun(arrow_660593299e_indi,nat),fun(nat,arrow_660593299e_indi)),hilbert_inv_into(arrow_660593299e_indi,nat),top_top(fun(arrow_660593299e_indi,bool))),h),n)))),
    c_0_2023,
    [final] ).

cnf(c_0_2986,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X4))
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,X2,esk91_4(X1,X3,X4,X2))),hAPP(nat,X1,X2,hAPP(nat,nat,suc,esk91_4(X1,X3,X4,X2)))))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,X2,X3)),hAPP(nat,X1,X2,X4))) ),
    c_0_2024,
    [final] ).

cnf(c_0_2987,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X4)),X5))
    | ~ hBOOL(hAPP(fun(fun(X2,X1),bool),bool,hAPP(fun(X2,X1),fun(fun(fun(X2,X1),bool),bool),member(fun(X2,X1)),X3),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,X1),bool),hAPP(fun(X2,bool),fun(fun(X2,fun(X1,bool)),fun(fun(X2,X1),bool)),pi(X2,X1),X4),hAPP(fun(X1,bool),fun(X2,fun(X1,bool)),combk(fun(X1,bool),X2),X5)))) ),
    c_0_2025,
    [final] ).

cnf(c_0_2988,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1) ),
    c_0_2026,
    [final] ).

cnf(c_0_2989,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2) ),
    c_0_2027,
    [final] ).

cnf(c_0_2990,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1) ),
    c_0_2028,
    [final] ).

cnf(c_0_2991,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2) ),
    c_0_2029,
    [final] ).

cnf(c_0_2992,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X1) ),
    c_0_2030,
    [final] ).

cnf(c_0_2993,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X2) ),
    c_0_2031,
    [final] ).

cnf(c_0_2994,plain,
    ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),esk12_1(X1)),esk13_1(X1))),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),esk11_1(X1),X2)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),esk12_1(X1)),esk13_1(X1))),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),esk10_1(X1),X2))) ),
    c_0_2032,
    [final] ).

cnf(c_0_2995,plain,
    ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),esk12_1(X1)),esk13_1(X1))),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),esk10_1(X1),X2)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),esk12_1(X1)),esk13_1(X1))),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),esk11_1(X1),X2))) ),
    c_0_2033,
    [final] ).

cnf(c_0_2996,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X3),X4)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X4)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3)) ),
    c_0_2034,
    [final] ).

cnf(c_0_2997,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X3),X4)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3)) ),
    c_0_2035,
    [final] ).

cnf(c_0_2998,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X3),X4)))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3)) ),
    c_0_2036,
    [final] ).

cnf(c_0_2999,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X3),X4)))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3)) ),
    c_0_2037,
    [final] ).

cnf(c_0_3000,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X5))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),top_top(fun(X1,bool))))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X4)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X5))) ),
    c_0_2038,
    [final] ).

cnf(c_0_3001,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,X2,X3)),hAPP(nat,X1,X2,X4)))
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,X2,esk91_4(X1,X3,X4,X2))),hAPP(nat,X1,X2,hAPP(nat,nat,suc,esk91_4(X1,X3,X4,X2)))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X4)) ),
    c_0_2039,
    [final] ).

cnf(c_0_3002,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,X2,X3)),hAPP(nat,X1,X2,X4)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,X2,esk90_4(X1,X3,X4,X2))),hAPP(nat,X1,X2,hAPP(nat,nat,suc,esk90_4(X1,X3,X4,X2)))))
    | ~ order(X1) ),
    c_0_2040,
    [final] ).

cnf(c_0_3003,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,X2,X3)),hAPP(nat,X1,X2,X4)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,X2,esk89_4(X1,X3,X4,X2))),hAPP(nat,X1,X2,hAPP(nat,nat,suc,esk89_4(X1,X3,X4,X2)))))
    | ~ order(X1) ),
    c_0_2041,
    [final] ).

cnf(c_0_3004,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    c_0_2042,
    [final] ).

cnf(c_0_3005,plain,
    ( hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),hAPP(fun(nat,bool),nat,finite_card(nat),X1))) = X1
    | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),X1),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),hAPP(fun(nat,bool),nat,finite_card(nat),X1))))) ),
    c_0_2043,
    [final] ).

cnf(c_0_3006,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X2)),hAPP(fun(X3,bool),nat,finite_card(X3),X4)))
    | ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X5),X2))
    | ~ hBOOL(hAPP(fun(fun(X1,X3),bool),bool,hAPP(fun(X1,X3),fun(fun(fun(X1,X3),bool),bool),member(fun(X1,X3)),X5),hAPP(fun(X1,fun(X3,bool)),fun(fun(X1,X3),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X3,bool)),fun(fun(X1,X3),bool)),pi(X1,X3),X2),hAPP(fun(X3,bool),fun(X1,fun(X3,bool)),combk(fun(X3,bool),X1),X4)))) ),
    c_0_2044,
    [final] ).

cnf(c_0_3007,plain,
    ( ti(X1,X2) = ti(X1,X3)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(fun(X4,bool),fun(X1,bool),hAPP(fun(X4,X1),fun(fun(X4,bool),fun(X1,bool)),image(X4,X1),X5),X6)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X4,bool),fun(X1,bool),hAPP(fun(X4,X1),fun(fun(X4,bool),fun(X1,bool)),image(X4,X1),X5),X6)))
    | hAPP(X1,X4,hAPP(fun(X4,X1),fun(X1,X4),hAPP(fun(X4,bool),fun(fun(X4,X1),fun(X1,X4)),hilbert_inv_into(X4,X1),X6),X5),X2) != hAPP(X1,X4,hAPP(fun(X4,X1),fun(X1,X4),hAPP(fun(X4,bool),fun(fun(X4,X1),fun(X1,X4)),hilbert_inv_into(X4,X1),X6),X5),X3) ),
    c_0_2045,
    [final] ).

cnf(c_0_3008,plain,
    ( hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),member(product_prod(X1,X2)),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X5),X6)),X4))
    | ti(fun(product_prod(X1,X2),bool),X3) != ti(fun(product_prod(X1,X2),bool),X4)
    | ~ hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),member(product_prod(X1,X2)),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X5),X6)),X3)) ),
    c_0_2046,
    [final] ).

cnf(c_0_3009,plain,
    ( hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),member(product_prod(X1,X2)),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X5),X6)),X3))
    | ti(fun(product_prod(X1,X2),bool),X3) != ti(fun(product_prod(X1,X2),bool),X4)
    | ~ hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),member(product_prod(X1,X2)),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X5),X6)),X4)) ),
    c_0_2047,
    [final] ).

cnf(c_0_3010,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X2,X1,X3,X4)),X5))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X4),X6))
    | ~ hBOOL(hAPP(fun(fun(X2,X1),bool),bool,hAPP(fun(X2,X1),fun(fun(fun(X2,X1),bool),bool),member(fun(X2,X1)),X3),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,X1),bool),hAPP(fun(X2,bool),fun(fun(X2,fun(X1,bool)),fun(fun(X2,X1),bool)),pi(X2,X1),X6),hAPP(fun(X1,bool),fun(X2,fun(X1,bool)),combk(fun(X1,bool),X2),X5)))) ),
    c_0_2048,
    [final] ).

cnf(c_0_3011,plain,
    ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(fun(X1,X2),bool),fun(fun(fun(X1,X2),bool),bool),ord_less_eq(fun(fun(X1,X2),bool)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X3),X4)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X5),X4)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X5),X3)) ),
    c_0_2049,
    [final] ).

cnf(c_0_3012,plain,
    ( ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X2)),X1))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),X1))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X1),arrow_2064824852le_Lin)) ),
    c_0_2050,
    [final] ).

cnf(c_0_3013,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    c_0_2051,
    [final] ).

cnf(c_0_3014,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(X1,bool)),combc(X1,fun(X1,bool),bool),member(X1)),X2)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(X1,bool)),combc(X1,fun(X1,bool),bool),member(X1)),X3)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
    c_0_2052,
    [final] ).

cnf(c_0_3015,plain,
    ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),esk12_1(X1)),esk13_1(X1))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,esk11_1(X1))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),esk12_1(X1)),esk13_1(X1))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,esk10_1(X1)))) ),
    c_0_2053,
    [final] ).

cnf(c_0_3016,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,X1,X2)),X3)),hAPP(nat,nat,X1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3))))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk61_3(X2,X3,X1)),esk62_3(X2,X3,X1))) ),
    c_0_2054,
    [final] ).

cnf(c_0_3017,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    c_0_2055,
    [final] ).

cnf(c_0_3018,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    c_0_2056,
    [final] ).

cnf(c_0_3019,plain,
    ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X3),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X4),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),X5))))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk65_5(X2,X1,X3,X5,X4)),X4)) ),
    c_0_2057,
    [final] ).

cnf(c_0_3020,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X2))
    | ~ linorder(X1)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5))) ),
    c_0_2058,
    [final] ).

cnf(c_0_3021,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
    | ~ linorder(X1)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5))) ),
    c_0_2059,
    [final] ).

cnf(c_0_3022,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X4))),hAPP(fun(X2,bool),nat,finite_card(X2),X4)))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4)) ),
    c_0_2060,
    [final] ).

cnf(c_0_3023,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X3),X4)))
    | ti(arrow_490897120le_alt,X1) != ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X2) != ti(arrow_490897120le_alt,X4) ),
    c_0_2061,
    [final] ).

cnf(c_0_3024,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X3),X4)))
    | ti(arrow_490897120le_alt,X1) != ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X1) != ti(arrow_490897120le_alt,X4) ),
    c_0_2062,
    [final] ).

cnf(c_0_3025,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X3),X4)))
    | ti(arrow_490897120le_alt,X1) != ti(arrow_490897120le_alt,X4) ),
    c_0_2063,
    [final] ).

cnf(c_0_3026,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X3),X4)))
    | ti(arrow_490897120le_alt,X2) != ti(arrow_490897120le_alt,X4) ),
    c_0_2064,
    [final] ).

cnf(c_0_3027,plain,
    ( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X2),X3) = ti(fun(X1,bool),X3)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X2),X3)),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    c_0_2065,
    [final] ).

cnf(c_0_3028,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    c_0_2066,
    [final] ).

cnf(c_0_3029,plain,
    ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X4)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X5)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),top_top(fun(X1,bool))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X5)) ),
    c_0_2067,
    [final] ).

cnf(c_0_3030,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X2,X1,X3,X4)),hAPP(X2,fun(X1,bool),X5,X4)))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X4),X6))
    | ~ hBOOL(hAPP(fun(fun(X2,X1),bool),bool,hAPP(fun(X2,X1),fun(fun(fun(X2,X1),bool),bool),member(fun(X2,X1)),X3),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,X1),bool),hAPP(fun(X2,bool),fun(fun(X2,fun(X1,bool)),fun(fun(X2,X1),bool)),pi(X2,X1),X6),X5))) ),
    c_0_2068,
    [final] ).

cnf(c_0_3031,plain,
    ( hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),hAPP(X1,X4,X5,X2)),hAPP(X1,fun(X4,bool),X6,X2)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
    | ~ hBOOL(hAPP(fun(fun(X1,X4),bool),bool,hAPP(fun(X1,X4),fun(fun(fun(X1,X4),bool),bool),member(fun(X1,X4)),X5),hAPP(fun(X1,fun(X4,bool)),fun(fun(X1,X4),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X4,bool)),fun(fun(X1,X4),bool)),pi(X1,X4),X3),X6))) ),
    c_0_2069,
    [final] ).

cnf(c_0_3032,plain,
    ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),esk102_5(X1,X3,X2,X4,X5)),X5))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5))) ),
    c_0_2070,
    [final] ).

cnf(c_0_3033,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X4)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X5)))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less(fun(X2,bool)),X4),X5))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),inj_on(X2,X1),X3),X5)) ),
    c_0_2071,
    [final] ).

cnf(c_0_3034,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(bool,bool),fun(fun(X1,bool),fun(X1,bool)),combb(bool,bool,X1),fNot),X2)))) ),
    c_0_2072,
    [final] ).

cnf(c_0_3035,plain,
    ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),esk101_5(X1,X3,X2,X4,X5)),X5))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5))) ),
    c_0_2073,
    [final] ).

cnf(c_0_3036,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(product_prod(X2,X1),bool),fun(X2,fun(X1,bool)),in_rel(X2,X1),X3),X4),X5))
    | ~ hBOOL(hAPP(fun(product_prod(X2,X1),bool),bool,hAPP(product_prod(X2,X1),fun(fun(product_prod(X2,X1),bool),bool),member(product_prod(X2,X1)),hAPP(X1,product_prod(X2,X1),hAPP(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),X4),X5)),X3)) ),
    c_0_2074,
    [final] ).

cnf(c_0_3037,plain,
    ( hBOOL(hAPP(fun(fun(X1,bool),bool),bool,finite_finite_1(fun(X1,bool)),hAPP(fun(fun(X1,bool),bool),fun(fun(X1,bool),bool),collect(fun(X1,bool)),hAPP(fun(X1,bool),fun(fun(X1,bool),bool),hAPP(fun(fun(X1,bool),fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(fun(X1,bool),bool)),combc(fun(X1,bool),fun(X1,bool),bool),ord_less_eq(fun(X1,bool))),X2))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
    c_0_2075,
    [final] ).

cnf(c_0_3038,plain,
    ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X3),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X4),X5)))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk68_5(X2,X1,X3,X5,X4)),X4)) ),
    c_0_2076,
    [final] ).

cnf(c_0_3039,plain,
    ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X3),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X4),X5)))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk33_5(X2,X1,X3,X5,X4)),X4)) ),
    c_0_2077,
    [final] ).

cnf(c_0_3040,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,fun(X2,X3)),fun(fun(X1,bool),bool),inj_on(X1,fun(X2,X3)),hAPP(fun(X1,X3),fun(X1,fun(X2,X3)),hAPP(fun(X3,fun(X2,X3)),fun(fun(X1,X3),fun(X1,fun(X2,X3))),combb(X3,fun(X2,X3),X1),combk(X3,X2)),X4)),top_top(fun(X1,bool))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X4),top_top(fun(X1,bool)))) ),
    c_0_2078,
    [final] ).

cnf(c_0_3041,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    c_0_2079,
    [final] ).

cnf(c_0_3042,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    c_0_2080,
    [final] ).

cnf(c_0_3043,plain,
    ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,X1))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),esk16_1(X1)),esk17_1(X1))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,esk15_1(X1)))) ),
    c_0_2081,
    [final] ).

cnf(c_0_3044,plain,
    ( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X1),X2)),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X1),arrow_2064824852le_Lin)) ),
    c_0_2082,
    [final] ).

cnf(c_0_3045,plain,
    ( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X1),X2)),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X1),arrow_2064824852le_Lin)) ),
    c_0_2083,
    [final] ).

cnf(c_0_3046,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    c_0_2084,
    [final] ).

cnf(c_0_3047,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ ordere236663937imp_le(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4))) ),
    c_0_2085,
    [final] ).

cnf(c_0_3048,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ ordere236663937imp_le(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3))) ),
    c_0_2086,
    [final] ).

cnf(c_0_3049,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)))
    | ~ ordere236663937imp_le(X1) ),
    c_0_2087,
    [final] ).

cnf(c_0_3050,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)))
    | ~ ordere236663937imp_le(X1) ),
    c_0_2088,
    [final] ).

cnf(c_0_3051,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ ordere236663937imp_le(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4))) ),
    c_0_2089,
    [final] ).

cnf(c_0_3052,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ ordere236663937imp_le(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3))) ),
    c_0_2090,
    [final] ).

cnf(c_0_3053,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)))
    | ~ ordere236663937imp_le(X1) ),
    c_0_2091,
    [final] ).

cnf(c_0_3054,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)))
    | ~ ordere236663937imp_le(X1) ),
    c_0_2092,
    [final] ).

cnf(c_0_3055,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X4)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X5)))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X4),X5)) ),
    c_0_2093,
    [final] ).

cnf(c_0_3056,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X2))) ),
    c_0_2094,
    [final] ).

cnf(c_0_3057,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X2))) ),
    c_0_2095,
    [final] ).

cnf(c_0_3058,plain,
    ( hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less_eq(fun(X1,X2)),X3),X4))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,esk39_4(X1,X2,X3,X4))),hAPP(X1,X2,X4,esk39_4(X1,X2,X3,X4))))
    | ~ ord(X2) ),
    c_0_2096,
    [final] ).

cnf(c_0_3059,plain,
    ( hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X4))
    | ~ ord(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X3,esk29_4(X2,X1,X3,X4))),hAPP(X2,X1,X4,esk29_4(X2,X1,X3,X4)))) ),
    c_0_2097,
    [final] ).

cnf(c_0_3060,plain,
    ( hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),member(product_prod(X1,X2)),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X3),X4)),X5))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),hAPP(fun(product_prod(X1,X2),bool),fun(X1,fun(X2,bool)),in_rel(X1,X2),X5),X3),X4)) ),
    c_0_2098,
    [final] ).

cnf(c_0_3061,plain,
    ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),combk(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),arrow_660593299e_indi),X1)),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X1),arrow_2064824852le_Lin)) ),
    c_0_2099,
    [final] ).

cnf(c_0_3062,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    c_0_2100,
    [final] ).

cnf(c_0_3063,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk71_5(X2,X1,X3,X4,X5)),X5))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X4),X5))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X5)) ),
    c_0_2101,
    [final] ).

cnf(c_0_3064,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk71_5(X2,X1,X3,X4,X5)),X5))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X5))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X4),X5)) ),
    c_0_2102,
    [final] ).

cnf(c_0_3065,plain,
    ( hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X2) = hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X2,X3)
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X2),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,X1),X3)) ),
    c_0_2103,
    [final] ).

cnf(c_0_3066,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X5)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | ~ ordere223160158up_add(X1) ),
    c_0_2104,
    [final] ).

cnf(c_0_3067,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X5)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | ~ ordere779506340up_add(X1) ),
    c_0_2105,
    [final] ).

cnf(c_0_3068,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X5)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | ~ ordere223160158up_add(X1) ),
    c_0_2106,
    [final] ).

cnf(c_0_3069,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X5)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | ~ ordere223160158up_add(X1) ),
    c_0_2107,
    [final] ).

cnf(c_0_3070,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X1,X2)),hAPP(nat,nat,X1,X3)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,X1,esk63_3(X2,X3,X1))),hAPP(nat,nat,X1,esk64_3(X2,X3,X1)))) ),
    c_0_2108,
    [final] ).

cnf(c_0_3071,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X4)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X4))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3)) ),
    c_0_2109,
    [final] ).

cnf(c_0_3072,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X4)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X4))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X3)) ),
    c_0_2110,
    [final] ).

cnf(c_0_3073,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(bool,bool),fun(fun(X1,bool),fun(X1,bool)),combb(bool,bool,X1),fNot),X2))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool)))) ),
    c_0_2111,
    [final] ).

cnf(c_0_3074,plain,
    ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab)),
    c_0_2112,
    [final] ).

cnf(c_0_3075,plain,
    ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba)),
    c_0_2113,
    [final] ).

cnf(c_0_3076,plain,
    ( hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),hAPP(fun(X1,X2),fun(X2,X1),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)),hilbert_inv_into(X1,X2),top_top(fun(X1,bool))),X3)),X4)) = ti(fun(X2,bool),X4)
    | hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),top_top(fun(X1,bool))) != top_top(fun(X2,bool)) ),
    c_0_2114,
    [final] ).

cnf(c_0_3077,plain,
    ( hAPP(X1,X2,X3,hAPP(X2,X1,hAPP(fun(X1,X2),fun(X2,X1),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)),hilbert_inv_into(X1,X2),X4),X3),X5)) = ti(X2,X5)
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X5),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X4))) ),
    c_0_2115,
    [final] ).

cnf(c_0_3078,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    c_0_2116,
    [final] ).

cnf(c_0_3079,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X3),X4)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X2) != ti(arrow_490897120le_alt,X4) ),
    c_0_2117,
    [final] ).

cnf(c_0_3080,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X3),X4)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X2) != ti(arrow_490897120le_alt,X4) ),
    c_0_2118,
    [final] ).

cnf(c_0_3081,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X3),X4)))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) != ti(arrow_490897120le_alt,X4) ),
    c_0_2119,
    [final] ).

cnf(c_0_3082,plain,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X3),X4)))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X1) != ti(arrow_490897120le_alt,X4) ),
    c_0_2120,
    [final] ).

cnf(c_0_3083,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
    | ~ linordered_idom(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)),zero_zero(X1))) ),
    c_0_2121,
    [final] ).

cnf(c_0_3084,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
    | ~ linord219039673up_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)),zero_zero(X1))) ),
    c_0_2122,
    [final] ).

cnf(c_0_3085,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1)))
    | ~ linord219039673up_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)),zero_zero(X1))) ),
    c_0_2123,
    [final] ).

cnf(c_0_3086,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),ring_1_Ints(X1)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),ring_1_Ints(X1)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),ring_1_Ints(X1)))
    | ~ ring_1(X1) ),
    c_0_2124,
    [final] ).

cnf(c_0_3087,plain,
    ( hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),esk102_5(X1,X3,X2,X4,X5)) = ti(fun(X1,bool),X2)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5))) ),
    c_0_2125,
    [final] ).

cnf(c_0_3088,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X2)),hAPP(fun(X1,bool),nat,finite_card(X1),X3)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    c_0_2126,
    [final] ).

cnf(c_0_3089,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X3)),X2)) ),
    c_0_2127,
    [final] ).

cnf(c_0_3090,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X1)),X2)) ),
    c_0_2128,
    [final] ).

cnf(c_0_3091,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X3)),X2)) ),
    c_0_2129,
    [final] ).

cnf(c_0_3092,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),X3)) ),
    c_0_2130,
    [final] ).

cnf(c_0_3093,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),X3)) ),
    c_0_2131,
    [final] ).

cnf(c_0_3094,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)))
    | ~ ordere236663937imp_le(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4)) ),
    c_0_2132,
    [final] ).

cnf(c_0_3095,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)))
    | ~ ordere236663937imp_le(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4)) ),
    c_0_2133,
    [final] ).

cnf(c_0_3096,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | ~ ordere223160158up_add(X1) ),
    c_0_2134,
    [final] ).

cnf(c_0_3097,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
    | ~ ordere223160158up_add(X1) ),
    c_0_2135,
    [final] ).

cnf(c_0_3098,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)))
    | ~ ordere236663937imp_le(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4)) ),
    c_0_2136,
    [final] ).

cnf(c_0_3099,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)))
    | ~ ordere236663937imp_le(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4)) ),
    c_0_2137,
    [final] ).

cnf(c_0_3100,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | ~ ordere779506340up_add(X1) ),
    c_0_2138,
    [final] ).

cnf(c_0_3101,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
    | ~ ordere779506340up_add(X1) ),
    c_0_2139,
    [final] ).

cnf(c_0_3102,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X4),X5))
    | hAPP(X1,X2,X3,esk71_5(X2,X1,X3,X4,X5)) != hAPP(X1,X2,X4,esk71_5(X2,X1,X3,X4,X5))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X5)) ),
    c_0_2140,
    [final] ).

cnf(c_0_3103,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X5))
    | hAPP(X1,X2,X3,esk71_5(X2,X1,X3,X4,X5)) != hAPP(X1,X2,X4,esk71_5(X2,X1,X3,X4,X5))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X4),X5)) ),
    c_0_2141,
    [final] ).

cnf(c_0_3104,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3)) ),
    c_0_2142,
    [final] ).

cnf(c_0_3105,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X3)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3)) ),
    c_0_2143,
    [final] ).

cnf(c_0_3106,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X3)) ),
    c_0_2144,
    [final] ).

cnf(c_0_3107,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X3)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3)) ),
    c_0_2145,
    [final] ).

cnf(c_0_3108,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X2),X3)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    c_0_2146,
    [final] ).

cnf(c_0_3109,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),zero_zero(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),zero_zero(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
    | ~ ordere216010020id_add(X1) ),
    c_0_2147,
    [final] ).

cnf(c_0_3110,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),zero_zero(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),zero_zero(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1)))
    | ~ ordere216010020id_add(X1) ),
    c_0_2148,
    [final] ).

cnf(c_0_3111,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),zero_zero(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),zero_zero(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
    | ~ ordere216010020id_add(X1) ),
    c_0_2149,
    [final] ).

cnf(c_0_3112,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),zero_zero(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),zero_zero(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1)))
    | ~ ordere216010020id_add(X1) ),
    c_0_2150,
    [final] ).

cnf(c_0_3113,plain,
    ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,X1))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),esk16_1(X1)),esk17_1(X1))),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),esk15_1(X1),X2))) ),
    c_0_2151,
    [final] ).

cnf(c_0_3114,plain,
    ( hAPP(X3,X1,X4,esk101_5(X1,X3,X2,X4,X5)) = ti(X1,X2)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5))) ),
    c_0_2152,
    [final] ).

cnf(c_0_3115,plain,
    hBOOL(hAPP(fun(fun(X1,X1),bool),bool,hAPP(fun(X1,X1),fun(fun(fun(X1,X1),bool),bool),member(fun(X1,X1)),combi(X1)),hAPP(fun(X1,fun(X1,bool)),fun(fun(X1,X1),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X1,bool)),fun(fun(X1,X1),bool)),pi(X1,X1),X2),hAPP(fun(X1,bool),fun(X1,fun(X1,bool)),combk(fun(X1,bool),X1),X2)))),
    c_0_2153,
    [final] ).

cnf(c_0_3116,plain,
    ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),X2)),
    c_0_2154,
    [final] ).

cnf(c_0_3117,plain,
    ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),X1)),
    c_0_2155,
    [final] ).

cnf(c_0_3118,plain,
    ( hAPP(fun(X1,bool),nat,hAPP(nat,fun(fun(X1,bool),nat),hAPP(fun(X1,nat),fun(nat,fun(fun(X1,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(X1,nat),fun(nat,fun(fun(X1,bool),nat))),finite_fold_image(nat,X1),plus_plus(nat)),hAPP(nat,fun(X1,nat),combk(nat,X1),one_one(nat))),zero_zero(nat)),X2) = hAPP(fun(X1,bool),nat,finite_card(X1),X2)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
    c_0_2156,
    [final] ).

cnf(c_0_3119,plain,
    ( hAPP(fun(X1,bool),nat,hAPP(nat,fun(fun(X1,bool),nat),hAPP(fun(X1,nat),fun(nat,fun(fun(X1,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(X1,nat),fun(nat,fun(fun(X1,bool),nat))),finite_fold_image(nat,X1),plus_plus(nat)),hAPP(nat,fun(X1,nat),combk(nat,X1),one_one(nat))),zero_zero(nat)),X2) = hAPP(fun(X1,bool),nat,finite_card(X1),X2)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
    c_0_2157,
    [final] ).

cnf(c_0_3120,plain,
    ( ti(fun(X1,bool),X2) = ti(fun(X1,bool),X3)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X3)),hAPP(fun(X1,bool),nat,finite_card(X1),X2)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    c_0_2158,
    [final] ).

cnf(c_0_3121,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5)))
    | ti(fun(X1,bool),X2) != hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X6)
    | ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X6),X5)) ),
    c_0_2159,
    [final] ).

cnf(c_0_3122,plain,
    hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,nat),fun(fun(nat,bool),bool),inj_on(nat,nat),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),X1)),X2)),
    c_0_2160,
    [final] ).

cnf(c_0_3123,plain,
    hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),X1)))),
    c_0_2161,
    [final] ).

cnf(c_0_3124,plain,
    hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X1)))),
    c_0_2162,
    [final] ).

cnf(c_0_3125,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X5)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X5))
    | ~ comm_semiring_1(X1) ),
    c_0_2163,
    [final] ).

cnf(c_0_3126,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X2,X1,X3,X4)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X5)))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X4),X5)) ),
    c_0_2164,
    [final] ).

cnf(c_0_3127,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)),zero_zero(X1)))
    | ~ linordered_idom(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1))) ),
    c_0_2165,
    [final] ).

cnf(c_0_3128,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)),zero_zero(X1)))
    | ~ linord219039673up_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1))) ),
    c_0_2166,
    [final] ).

cnf(c_0_3129,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)),zero_zero(X1)))
    | ~ linord219039673up_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1))) ),
    c_0_2167,
    [final] ).

cnf(c_0_3130,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X1))) ),
    c_0_2168,
    [final] ).

cnf(c_0_3131,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ hBOOL(hAPP(fun(sum_sum(X3,X1),bool),bool,finite_finite_1(sum_sum(X3,X1)),hAPP(fun(X1,bool),fun(sum_sum(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X1,bool),fun(sum_sum(X3,X1),bool)),sum_Plus(X3,X1),X4),X2))) ),
    c_0_2169,
    [final] ).

cnf(c_0_3132,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ hBOOL(hAPP(fun(sum_sum(X1,X3),bool),bool,finite_finite_1(sum_sum(X1,X3)),hAPP(fun(X3,bool),fun(sum_sum(X1,X3),bool),hAPP(fun(X1,bool),fun(fun(X3,bool),fun(sum_sum(X1,X3),bool)),sum_Plus(X1,X3),X2),X4))) ),
    c_0_2170,
    [final] ).

cnf(c_0_3133,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3))
    | ~ hBOOL(hAPP(fun(sum_sum(X1,X2),bool),bool,finite_finite_1(sum_sum(X1,X2)),hAPP(fun(X2,bool),fun(sum_sum(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X2,bool),fun(sum_sum(X1,X2),bool)),sum_Plus(X1,X2),X3),X4))) ),
    c_0_2171,
    [final] ).

cnf(c_0_3134,plain,
    ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
    | ~ hBOOL(hAPP(fun(sum_sum(X1,X2),bool),bool,finite_finite_1(sum_sum(X1,X2)),hAPP(fun(X2,bool),fun(sum_sum(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X2,bool),fun(sum_sum(X1,X2),bool)),sum_Plus(X1,X2),X3),X4))) ),
    c_0_2172,
    [final] ).

cnf(c_0_3135,plain,
    ( hBOOL(hAPP(fun(X1,fun(X2,bool)),bool,hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,fun(X2,bool)),bool),ord_less_eq(fun(X1,fun(X2,bool))),X3),X4))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X4,esk50_4(X2,X1,X4,X3)),esk51_4(X2,X1,X4,X3))) ),
    c_0_2173,
    [final] ).

cnf(c_0_3136,plain,
    ( hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,X1),X2))
    | hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),esk32_2(X1,X2)),arrow_1111136790e_Prof)) ),
    c_0_2174,
    [final] ).

cnf(c_0_3137,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
    | ~ ordere216010020id_add(X1) ),
    c_0_2175,
    [final] ).

cnf(c_0_3138,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
    | ~ ordere216010020id_add(X1) ),
    c_0_2176,
    [final] ).

cnf(c_0_3139,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
    | ~ ordere216010020id_add(X1) ),
    c_0_2177,
    [final] ).

cnf(c_0_3140,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
    | ~ ordere216010020id_add(X1) ),
    c_0_2178,
    [final] ).

cnf(c_0_3141,plain,
    hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),combb(X3,X2,X1),X4),X5)),top_top(fun(X1,bool))) = hAPP(fun(X3,bool),fun(X2,bool),hAPP(fun(X3,X2),fun(fun(X3,bool),fun(X2,bool)),image(X3,X2),X4),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X5),top_top(fun(X1,bool)))),
    c_0_2179,
    [final] ).

cnf(c_0_3142,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),esk26_2(X1,X2))) ),
    c_0_2180,
    [final] ).

cnf(c_0_3143,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
    | ~ ordere216010020id_add(X1) ),
    c_0_2181,
    [final] ).

cnf(c_0_3144,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
    | ~ ordere216010020id_add(X1) ),
    c_0_2182,
    [final] ).

cnf(c_0_3145,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
    | ~ linordered_semidom(X1) ),
    c_0_2183,
    [final] ).

cnf(c_0_3146,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
    | ~ ordere216010020id_add(X1) ),
    c_0_2184,
    [final] ).

cnf(c_0_3147,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X4))
    | ~ ordere216010020id_add(X1) ),
    c_0_2185,
    [final] ).

cnf(c_0_3148,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ linordered_field(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),esk99_3(X1,X2,X3)))) ),
    c_0_2186,
    [final] ).

cnf(c_0_3149,plain,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),esk19_0)),
    c_0_2187,
    [final] ).

cnf(c_0_3150,plain,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),esk18_0)),
    c_0_2188,
    [final] ).

cnf(c_0_3151,plain,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba)),
    c_0_2189,
    [final] ).

cnf(c_0_3152,plain,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab)),
    c_0_2190,
    [final] ).

cnf(c_0_3153,plain,
    hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),hAPP(fun(X4,bool),fun(X1,bool),hAPP(fun(X4,X1),fun(fun(X4,bool),fun(X1,bool)),image(X4,X1),X5),X6)) = hAPP(fun(X4,bool),fun(X2,bool),hAPP(fun(X4,X2),fun(fun(X4,bool),fun(X2,bool)),image(X4,X2),hAPP(fun(X4,X1),fun(X4,X2),hAPP(fun(X1,X2),fun(fun(X4,X1),fun(X4,X2)),combb(X1,X2,X4),X3),X5)),X6),
    c_0_2191,
    [final] ).

cnf(c_0_3154,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
    | ~ dense_linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),esk38_4(X1,X4,X2,X3)),X4)) ),
    c_0_2192,
    [final] ).

cnf(c_0_3155,plain,
    ( ti(X1,X2) = ti(X1,X3)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
    | hAPP(X1,X5,X6,X2) != hAPP(X1,X5,X6,X3)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X5),fun(fun(X1,bool),bool),inj_on(X1,X5),X6),X4)) ),
    c_0_2193,
    [final] ).

cnf(c_0_3156,plain,
    ( ti(X1,X5) = ti(X1,X6)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X4))
    | hAPP(X1,X2,X3,X5) != hAPP(X1,X2,X3,X6) ),
    c_0_2194,
    [final] ).

cnf(c_0_3157,plain,
    ( ti(X1,X4) = ti(X1,X5)
    | hAPP(X1,X2,X3,X4) != hAPP(X1,X2,X3,X5)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X6))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X6))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X6)) ),
    c_0_2195,
    [final] ).

cnf(c_0_3158,plain,
    ( ti(X1,X2) = ti(X1,X3)
    | hAPP(X1,X4,X5,X2) != hAPP(X1,X4,X5,X3)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X6))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X6))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X4),fun(fun(X1,bool),bool),inj_on(X1,X4),X5),X6)) ),
    c_0_2196,
    [final] ).

cnf(c_0_3159,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5)))
    | ti(X1,X2) != hAPP(X3,X1,X4,X6)
    | ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X5)) ),
    c_0_2197,
    [final] ).

cnf(c_0_3160,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5)))
    | ti(X1,X2) != hAPP(X3,X1,X4,X6)
    | ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X5)) ),
    c_0_2198,
    [final] ).

cnf(c_0_3161,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5)))
    | ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X5))
    | ti(X1,X2) != hAPP(X3,X1,X4,X6) ),
    c_0_2199,
    [final] ).

cnf(c_0_3162,plain,
    ( hBOOL(hAPP(product_prod(X1,X2),bool,X3,X4))
    | ~ hBOOL(hAPP(product_prod(X1,X2),bool,X3,hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),esk7_3(X1,X2,X3)),esk8_3(X1,X2,X3)))) ),
    c_0_2200,
    [final] ).

cnf(c_0_3163,plain,
    ( hAPP(X1,X2,X3,X5) = hAPP(X1,X2,X3,X6)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X4))
    | ti(X1,X5) != ti(X1,X6) ),
    c_0_2201,
    [final] ).

cnf(c_0_3164,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
    | ~ linord219039673up_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2))) ),
    c_0_2202,
    [final] ).

cnf(c_0_3165,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
    | ~ linord219039673up_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2))) ),
    c_0_2203,
    [final] ).

cnf(c_0_3166,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X1,X2)),hAPP(nat,nat,X1,X3)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk63_3(X2,X3,X1)),esk64_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3)) ),
    c_0_2204,
    [final] ).

cnf(c_0_3167,plain,
    ( hAPP(X1,X2,hAPP(fun(X2,X1),fun(X1,X2),hAPP(fun(X2,bool),fun(fun(X2,X1),fun(X1,X2)),hilbert_inv_into(X2,X1),X3),X4),hAPP(X2,X1,X4,X5)) = ti(X2,X5)
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X5),X3))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),inj_on(X2,X1),X4),X3)) ),
    c_0_2205,
    [final] ).

cnf(c_0_3168,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X3,X4),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X6,X4),X5))
    | ~ hBOOL(hAPP(fun(X2,fun(X1,bool)),bool,hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),bool),ord_less_eq(fun(X2,fun(X1,bool))),X6),X3)) ),
    c_0_2206,
    [final] ).

cnf(c_0_3169,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X3,X4),X5))
    | ~ hBOOL(hAPP(fun(X2,fun(X1,bool)),bool,hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),bool),ord_less_eq(fun(X2,fun(X1,bool))),X6),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X6,X4),X5)) ),
    c_0_2207,
    [final] ).

cnf(c_0_3170,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X2)),hAPP(fun(X1,bool),nat,finite_card(X1),X3)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    c_0_2208,
    [final] ).

cnf(c_0_3171,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X2)),hAPP(fun(X1,bool),nat,finite_card(X1),X3)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    c_0_2209,
    [final] ).

cnf(c_0_3172,plain,
    ( hAPP(X1,X2,hAPP(fun(X2,X1),fun(X1,X2),hAPP(fun(X2,bool),fun(fun(X2,X1),fun(X1,X2)),hilbert_inv_into(X2,X1),X3),X4),X5) = ti(X2,X6)
    | hAPP(X2,X1,X4,X6) != ti(X1,X5)
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X6),X3))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),inj_on(X2,X1),X4),X3)) ),
    c_0_2210,
    [final] ).

cnf(c_0_3173,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3)) ),
    c_0_2211,
    [final] ).

cnf(c_0_3174,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)))),
    c_0_2212,
    [final] ).

cnf(c_0_3175,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X1)))),
    c_0_2213,
    [final] ).

cnf(c_0_3176,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X4),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X4)) ),
    c_0_2214,
    [final] ).

cnf(c_0_3177,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X4)) ),
    c_0_2215,
    [final] ).

cnf(c_0_3178,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X4),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X4)) ),
    c_0_2216,
    [final] ).

cnf(c_0_3179,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X4)) ),
    c_0_2217,
    [final] ).

cnf(c_0_3180,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),hAPP(nat,nat,suc,X2))) ),
    c_0_2218,
    [final] ).

cnf(c_0_3181,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),hAPP(nat,nat,suc,X2))) ),
    c_0_2219,
    [final] ).

cnf(c_0_3182,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),hAPP(nat,nat,suc,X2))) ),
    c_0_2220,
    [final] ).

cnf(c_0_3183,plain,
    hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X2,X1,X3,X4)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),top_top(fun(X2,bool))))),
    c_0_2221,
    [final] ).

cnf(c_0_3184,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X5))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X5)) ),
    c_0_2222,
    [final] ).

cnf(c_0_3185,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X3)) ),
    c_0_2223,
    [final] ).

cnf(c_0_3186,plain,
    ( hAPP(fun(X1,X2),fun(X2,X1),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)),hilbert_inv_into(X1,X2),top_top(fun(X1,bool))),X3) = ti(fun(X2,X1),X4)
    | hAPP(X1,X2,X3,hAPP(X2,X1,X4,esk34_4(X1,X2,X4,X3))) != ti(X2,esk34_4(X1,X2,X4,X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),top_top(fun(X1,bool)))) ),
    c_0_2224,
    [final] ).

cnf(c_0_3187,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)),X3)
    | ~ comm_semiring_1(X1) ),
    c_0_2225,
    [final] ).

cnf(c_0_3188,plain,
    ( hBOOL(hAPP(fun(sum_sum(X1,X2),bool),bool,finite_finite_1(sum_sum(X1,X2)),hAPP(fun(X2,bool),fun(sum_sum(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X2,bool),fun(sum_sum(X1,X2),bool)),sum_Plus(X1,X2),X3),X4)))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    c_0_2226,
    [final] ).

cnf(c_0_3189,plain,
    ( hBOOL(hAPP(fun(sum_sum(X1,X2),bool),bool,finite_finite_1(sum_sum(X1,X2)),hAPP(fun(X2,bool),fun(sum_sum(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X2,bool),fun(sum_sum(X1,X2),bool)),sum_Plus(X1,X2),X3),X4)))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    c_0_2227,
    [final] ).

cnf(c_0_3190,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X4),X3)) ),
    c_0_2228,
    [final] ).

cnf(c_0_3191,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3)) ),
    c_0_2229,
    [final] ).

cnf(c_0_3192,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4)) ),
    c_0_2230,
    [final] ).

cnf(c_0_3193,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3)) ),
    c_0_2231,
    [final] ).

cnf(c_0_3194,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3)) ),
    c_0_2232,
    [final] ).

cnf(c_0_3195,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1)) ),
    c_0_2233,
    [final] ).

cnf(c_0_3196,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3)) ),
    c_0_2234,
    [final] ).

cnf(c_0_3197,plain,
    ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,X1))
    | hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),esk15_1(X1)),arrow_1111136790e_Prof)) ),
    c_0_2235,
    [final] ).

cnf(c_0_3198,plain,
    ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1))
    | hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),esk10_1(X1)),arrow_1111136790e_Prof)) ),
    c_0_2236,
    [final] ).

cnf(c_0_3199,plain,
    ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1))
    | hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),esk11_1(X1)),arrow_1111136790e_Prof)) ),
    c_0_2237,
    [final] ).

cnf(c_0_3200,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X3,X4)),hAPP(X2,X1,X5,X4)))
    | ~ ord(X1)
    | ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X5)) ),
    c_0_2238,
    [final] ).

cnf(c_0_3201,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X3,X4)),hAPP(X2,X1,X5,X4)))
    | ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X5))
    | ~ ord(X1) ),
    c_0_2239,
    [final] ).

cnf(c_0_3202,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X3,X4)),hAPP(X2,X1,X5,X4)))
    | ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X5))
    | ~ ord(X1) ),
    c_0_2240,
    [final] ).

cnf(c_0_3203,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X2)),X1)) ),
    c_0_2241,
    [final] ).

cnf(c_0_3204,plain,
    ( ti(X1,X2) = ti(X1,X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),X2))
    | hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X5),X2) != hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X3)
    | ~ linorder(X1) ),
    c_0_2242,
    [final] ).

cnf(c_0_3205,plain,
    ( ti(X1,X2) = ti(X1,X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X5))
    | hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X5) != hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X3),X4)
    | ~ linorder(X1) ),
    c_0_2243,
    [final] ).

cnf(c_0_3206,plain,
    ( ti(X1,X2) = ti(X1,X4)
    | ~ linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X5))
    | hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X3) != hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5) ),
    c_0_2244,
    [final] ).

cnf(c_0_3207,plain,
    ( ti(X1,X3) = ti(X1,X5)
    | ~ linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X5))
    | hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X3) != hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5) ),
    c_0_2245,
    [final] ).

cnf(c_0_3208,plain,
    ( hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less(fun(X2,X1)),X3),X4))
    | hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X4),X3))
    | ~ ord(X1)
    | ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X4)) ),
    c_0_2246,
    [final] ).

cnf(c_0_3209,plain,
    ( hBOOL(hAPP(fun(X1,fun(X2,bool)),bool,hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,fun(X2,bool)),bool),ord_less_eq(fun(X1,fun(X2,bool))),X3),X4))
    | hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X3,esk50_4(X2,X1,X4,X3)),esk51_4(X2,X1,X4,X3))) ),
    c_0_2247,
    [final] ).

cnf(c_0_3210,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),esk38_4(X1,X4,X2,X3)),X3))
    | ~ dense_linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    c_0_2248,
    [final] ).

cnf(c_0_3211,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)))
    | ~ linord219039673up_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2)) ),
    c_0_2249,
    [final] ).

cnf(c_0_3212,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)))
    | ~ linord219039673up_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2)) ),
    c_0_2250,
    [final] ).

cnf(c_0_3213,plain,
    ( hAPP(fun(sum_sum(X1,X2),bool),nat,finite_card(sum_sum(X1,X2)),hAPP(fun(X2,bool),fun(sum_sum(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X2,bool),fun(sum_sum(X1,X2),bool)),sum_Plus(X1,X2),X3),X4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X3)),hAPP(fun(X2,bool),nat,finite_card(X2),X4))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    c_0_2251,
    [final] ).

cnf(c_0_3214,plain,
    ( hAPP(fun(sum_sum(X1,X2),bool),nat,finite_card(sum_sum(X1,X2)),hAPP(fun(X2,bool),fun(sum_sum(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X2,bool),fun(sum_sum(X1,X2),bool)),sum_Plus(X1,X2),X3),X4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X3)),hAPP(fun(X2,bool),nat,finite_card(X2),X4))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    c_0_2252,
    [final] ).

cnf(c_0_3215,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X4),X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | hAPP(fun(X3,bool),nat,finite_card(X3),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X4),X2)) != hAPP(fun(X1,bool),nat,finite_card(X1),X2) ),
    c_0_2253,
    [final] ).

cnf(c_0_3216,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | hAPP(fun(X2,bool),nat,finite_card(X2),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X4)) != hAPP(fun(X1,bool),nat,finite_card(X1),X4)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4)) ),
    c_0_2254,
    [final] ).

cnf(c_0_3217,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
    c_0_2255,
    [final] ).

cnf(c_0_3218,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X2)) ),
    c_0_2256,
    [final] ).

cnf(c_0_3219,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    c_0_2257,
    [final] ).

cnf(c_0_3220,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X3)) ),
    c_0_2258,
    [final] ).

cnf(c_0_3221,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3)) ),
    c_0_2259,
    [final] ).

cnf(c_0_3222,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    c_0_2260,
    [final] ).

cnf(c_0_3223,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3)) ),
    c_0_2261,
    [final] ).

cnf(c_0_3224,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    c_0_2262,
    [final] ).

cnf(c_0_3225,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X3)) ),
    c_0_2263,
    [final] ).

cnf(c_0_3226,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    c_0_2264,
    [final] ).

cnf(c_0_3227,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1)) ),
    c_0_2265,
    [final] ).

cnf(c_0_3228,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),esk94_2(X1,X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),X2)) ),
    c_0_2266,
    [final] ).

cnf(c_0_3229,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),X2)) ),
    c_0_2267,
    [final] ).

cnf(c_0_3230,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),X2)) ),
    c_0_2268,
    [final] ).

cnf(c_0_3231,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),X2)) ),
    c_0_2269,
    [final] ).

cnf(c_0_3232,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),X2)) ),
    c_0_2270,
    [final] ).

cnf(c_0_3233,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),X2)) ),
    c_0_2271,
    [final] ).

cnf(c_0_3234,plain,
    ( hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X3) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5)
    | ~ linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X5))
    | ti(X1,X3) != ti(X1,X5)
    | ti(X1,X2) != ti(X1,X4) ),
    c_0_2272,
    [final] ).

cnf(c_0_3235,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),top_top(fun(X3,bool)))))
    | ti(X1,X2) != hAPP(X3,X1,X4,X5) ),
    c_0_2273,
    [final] ).

cnf(c_0_3236,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),hAPP(nat,nat,suc,X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    c_0_2274,
    [final] ).

cnf(c_0_3237,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),hAPP(nat,nat,suc,X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    c_0_2275,
    [final] ).

cnf(c_0_3238,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),hAPP(nat,nat,suc,X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    c_0_2276,
    [final] ).

cnf(c_0_3239,plain,
    ( hAPP(fun(X3,bool),nat,finite_card(X3),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X4),X2)) = hAPP(fun(X1,bool),nat,finite_card(X1),X2)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X4),X2)) ),
    c_0_2277,
    [final] ).

cnf(c_0_3240,plain,
    ( ~ ord(X1)
    | ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less(fun(X2,X1)),X3),X4))
    | ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X4),X3)) ),
    c_0_2278,
    [final] ).

cnf(c_0_3241,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),esk38_4(X1,X4,X2,X3)))
    | ~ dense_linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    c_0_2279,
    [final] ).

cnf(c_0_3242,plain,
    ( ti(fun(X1,bool),X2) = ti(fun(X1,bool),X3)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
    c_0_2280,
    [final] ).

cnf(c_0_3243,plain,
    ( ti(fun(X1,bool),X2) = ti(fun(X1,bool),X3)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
    c_0_2281,
    [final] ).

cnf(c_0_3244,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
    | ~ order(X1) ),
    c_0_2282,
    [final] ).

cnf(c_0_3245,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | ~ preorder(X1) ),
    c_0_2283,
    [final] ).

cnf(c_0_3246,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
    | ~ order(X1) ),
    c_0_2284,
    [final] ).

cnf(c_0_3247,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | ~ preorder(X1) ),
    c_0_2285,
    [final] ).

cnf(c_0_3248,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | ~ preorder(X1) ),
    c_0_2286,
    [final] ).

cnf(c_0_3249,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
    | ~ order(X1) ),
    c_0_2287,
    [final] ).

cnf(c_0_3250,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | ~ preorder(X1) ),
    c_0_2288,
    [final] ).

cnf(c_0_3251,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
    | ~ order(X1) ),
    c_0_2289,
    [final] ).

cnf(c_0_3252,plain,
    ( hAPP(X1,X2,hAPP(fun(X2,X1),fun(X1,X2),hAPP(fun(X2,bool),fun(fun(X2,X1),fun(X1,X2)),hilbert_inv_into(X2,X1),top_top(fun(X2,bool))),X3),hAPP(X2,X1,X3,X4)) = ti(X2,X4)
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),inj_on(X2,X1),X3),top_top(fun(X2,bool)))) ),
    c_0_2290,
    [final] ).

cnf(c_0_3253,plain,
    hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),p),arrow_1111136790e_Prof)),
    c_0_2291,
    [final] ).

cnf(c_0_3254,plain,
    ( hAPP(X1,X2,hAPP(fun(X2,X1),fun(X1,X2),hAPP(fun(X2,bool),fun(fun(X2,X1),fun(X1,X2)),hilbert_inv_into(X2,X1),top_top(fun(X2,bool))),X3),X4) = ti(X2,X5)
    | hAPP(X2,X1,X3,X5) != ti(X1,X4)
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),inj_on(X2,X1),X3),top_top(fun(X2,bool)))) ),
    c_0_2292,
    [final] ).

cnf(c_0_3255,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3)) ),
    c_0_2293,
    [final] ).

cnf(c_0_3256,plain,
    hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(arrow_660593299e_indi,bool),fun(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),top_top(fun(arrow_660593299e_indi,bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),arrow_660593299e_indi),arrow_2064824852le_Lin)) = arrow_1111136790e_Prof,
    c_0_2294,
    [final] ).

cnf(c_0_3257,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X3) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4),X2)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4),X3)) ),
    c_0_2295,
    [final] ).

cnf(c_0_3258,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4))
    | ~ comm_semiring_1(X1) ),
    c_0_2296,
    [final] ).

cnf(c_0_3259,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4))
    | ~ comm_semiring_1(X1) ),
    c_0_2297,
    [final] ).

cnf(c_0_3260,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4))
    | ~ ab_semigroup_add(X1) ),
    c_0_2298,
    [final] ).

cnf(c_0_3261,plain,
    ( X2 = X1
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),hAPP(nat,nat,suc,X1))) ),
    c_0_2299,
    [final] ).

cnf(c_0_3262,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),hAPP(nat,nat,suc,X1))) ),
    c_0_2300,
    [final] ).

cnf(c_0_3263,plain,
    ( X3 = X2
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3)) ),
    c_0_2301,
    [final] ).

cnf(c_0_3264,plain,
    ( ti(X1,X2) = zero_zero(X1)
    | ~ ordere216010020id_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) != zero_zero(X1) ),
    c_0_2302,
    [final] ).

cnf(c_0_3265,plain,
    ( ti(X1,X3) = zero_zero(X1)
    | ~ ordere216010020id_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) != zero_zero(X1) ),
    c_0_2303,
    [final] ).

cnf(c_0_3266,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),X3) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3)),
    c_0_2304,
    [final] ).

cnf(c_0_3267,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),X2))
    | hAPP(nat,nat,suc,X1) = X2
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    c_0_2305,
    [final] ).

cnf(c_0_3268,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) = zero_zero(X1)
    | ~ ordere216010020id_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
    | ti(X1,X3) != zero_zero(X1)
    | ti(X1,X2) != zero_zero(X1) ),
    c_0_2306,
    [final] ).

cnf(c_0_3269,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    c_0_2307,
    [final] ).

cnf(c_0_3270,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    c_0_2308,
    [final] ).

cnf(c_0_3271,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    c_0_2309,
    [final] ).

cnf(c_0_3272,plain,
    hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),X1))) = hAPP(nat,nat,suc,X1),
    c_0_2310,
    [final] ).

cnf(c_0_3273,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X4)))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4)) ),
    c_0_2311,
    [final] ).

cnf(c_0_3274,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk69_4(X2,X1,X3,X4)),X4)) ),
    c_0_2312,
    [final] ).

cnf(c_0_3275,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk70_4(X2,X1,X3,X4)),X4)) ),
    c_0_2313,
    [final] ).

cnf(c_0_3276,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk30_4(X1,X2,X3,X4)),X4)) ),
    c_0_2314,
    [final] ).

cnf(c_0_3277,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk31_4(X1,X2,X3,X4)),X4)) ),
    c_0_2315,
    [final] ).

cnf(c_0_3278,plain,
    ( X1 = hAPP(nat,nat,suc,X2)
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,suc,X2))) ),
    c_0_2316,
    [final] ).

cnf(c_0_3279,plain,
    ( X1 = hAPP(nat,nat,suc,X2)
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,suc,X2))) ),
    c_0_2317,
    [final] ).

cnf(c_0_3280,plain,
    ( hAPP(nat,nat,suc,esk94_2(X1,X2)) = X2
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),X2)) ),
    c_0_2318,
    [final] ).

cnf(c_0_3281,plain,
    ( hAPP(nat,nat,suc,esk92_2(X2,X1)) = X1
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X2)),X1)) ),
    c_0_2319,
    [final] ).

cnf(c_0_3282,plain,
    ( hBOOL(hAPP(nat,bool,X3,X1))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk86_3(X3,X1,X2)),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,X3,X2)) ),
    c_0_2320,
    [final] ).

cnf(c_0_3283,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ preorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    c_0_2321,
    [final] ).

cnf(c_0_3284,plain,
    hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X1))) = X1,
    c_0_2322,
    [final] ).

cnf(c_0_3285,plain,
    ( X1 = zero_zero(nat)
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk85_2(X1,X2)),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2))) ),
    c_0_2323,
    [final] ).

cnf(c_0_3286,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk53_3(X1,X3,X2)),X3)) ),
    c_0_2324,
    [final] ).

cnf(c_0_3287,plain,
    ( hBOOL(hAPP(product_prod(X1,X2),bool,X3,hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X4),X5)))
    | ~ hBOOL(hAPP(product_prod(X1,X2),bool,X3,esk6_3(X1,X2,X3))) ),
    c_0_2325,
    [final] ).

cnf(c_0_3288,plain,
    ( hBOOL(hAPP(nat,bool,X3,X1))
    | hBOOL(hAPP(nat,bool,X3,hAPP(nat,nat,suc,esk86_3(X3,X1,X2))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,X3,X2)) ),
    c_0_2326,
    [final] ).

cnf(c_0_3289,plain,
    ( hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X4))
    | ~ ord(X1)
    | ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less(fun(X2,X1)),X3),X4)) ),
    c_0_2327,
    [final] ).

cnf(c_0_3290,plain,
    ( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X2),top_top(fun(X1,bool))) = top_top(fun(X1,bool))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X2),top_top(fun(X1,bool))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool)))) ),
    c_0_2328,
    [final] ).

cnf(c_0_3291,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | X1 = X2
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1)) ),
    c_0_2329,
    [final] ).

cnf(c_0_3292,plain,
    ( X3 = X2
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3)) ),
    c_0_2330,
    [final] ).

cnf(c_0_3293,plain,
    ( X1 = X2
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2))) ),
    c_0_2331,
    [final] ).

cnf(c_0_3294,plain,
    ( X1 = X2
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),hAPP(nat,nat,suc,X1))) ),
    c_0_2332,
    [final] ).

cnf(c_0_3295,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | X1 = X2
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2))) ),
    c_0_2333,
    [final] ).

cnf(c_0_3296,plain,
    ( X1 = X2
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2))) ),
    c_0_2334,
    [final] ).

cnf(c_0_3297,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2))) ),
    c_0_2335,
    [final] ).

cnf(c_0_3298,plain,
    ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),X1)),
    c_0_2336,
    [final] ).

cnf(c_0_3299,plain,
    ( ti(fun(X1,bool),X2) = ti(fun(X1,bool),X3)
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
    c_0_2337,
    [final] ).

cnf(c_0_3300,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3))
    | ti(fun(X1,bool),X2) = ti(fun(X1,bool),X3)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
    c_0_2338,
    [final] ).

cnf(c_0_3301,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3)) ),
    c_0_2339,
    [final] ).

cnf(c_0_3302,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3)) ),
    c_0_2340,
    [final] ).

cnf(c_0_3303,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3)) ),
    c_0_2341,
    [final] ).

cnf(c_0_3304,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X2))
    | X1 != hAPP(nat,nat,suc,X3) ),
    c_0_2342,
    [final] ).

cnf(c_0_3305,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),esk75_1(X2)))
    | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X1),X2))
    | ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X2)) ),
    c_0_2343,
    [final] ).

cnf(c_0_3306,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),esk73_1(X2)))
    | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X1),X2))
    | ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X2)) ),
    c_0_2344,
    [final] ).

cnf(c_0_3307,plain,
    ( hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
    | hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),esk79_2(X2,X1)),one_one(nat))))
    | ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
    c_0_2345,
    [final] ).

cnf(c_0_3308,plain,
    ( ~ linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X2) != ti(X1,X3) ),
    c_0_2346,
    [final] ).

cnf(c_0_3309,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1)) ),
    c_0_2347,
    [final] ).

cnf(c_0_3310,plain,
    ( ti(X1,X2) = ti(X1,X3)
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    c_0_2348,
    [final] ).

cnf(c_0_3311,plain,
    ( ti(X1,X3) = ti(X1,X2)
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2)) ),
    c_0_2349,
    [final] ).

cnf(c_0_3312,plain,
    ( ti(X1,X2) = ti(X1,X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ order(X1) ),
    c_0_2350,
    [final] ).

cnf(c_0_3313,plain,
    ( ti(X1,X2) = ti(X1,X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ order(X1) ),
    c_0_2351,
    [final] ).

cnf(c_0_3314,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X2),top_top(fun(X1,bool))))
    | hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X2),top_top(fun(X1,bool))) != top_top(fun(X1,bool))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool)))) ),
    c_0_2352,
    [final] ).

cnf(c_0_3315,plain,
    ( hBOOL(X1)
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X3),X4))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X4),X3))
    | ~ preorder(X2) ),
    c_0_2353,
    [final] ).

cnf(c_0_3316,plain,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ linorder(X1) ),
    c_0_2354,
    [final] ).

cnf(c_0_3317,plain,
    ( ~ preorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2)) ),
    c_0_2355,
    [final] ).

cnf(c_0_3318,plain,
    ( ~ linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2)) ),
    c_0_2356,
    [final] ).

cnf(c_0_3319,plain,
    ( ~ linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2)) ),
    c_0_2357,
    [final] ).

cnf(c_0_3320,plain,
    ( ~ linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2)) ),
    c_0_2358,
    [final] ).

cnf(c_0_3321,plain,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ preorder(X1) ),
    c_0_2359,
    [final] ).

cnf(c_0_3322,plain,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ preorder(X1) ),
    c_0_2360,
    [final] ).

cnf(c_0_3323,plain,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ preorder(X1) ),
    c_0_2361,
    [final] ).

cnf(c_0_3324,plain,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ order(X1) ),
    c_0_2362,
    [final] ).

cnf(c_0_3325,plain,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ preorder(X1) ),
    c_0_2363,
    [final] ).

cnf(c_0_3326,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),hAPP(nat,nat,suc,X1)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | X2 != X1 ),
    c_0_2364,
    [final] ).

cnf(c_0_3327,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    c_0_2365,
    [final] ).

cnf(c_0_3328,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    c_0_2366,
    [final] ).

cnf(c_0_3329,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    c_0_2367,
    [final] ).

cnf(c_0_3330,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    c_0_2368,
    [final] ).

cnf(c_0_3331,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,suc,X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    c_0_2369,
    [final] ).

cnf(c_0_3332,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,suc,X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    c_0_2370,
    [final] ).

cnf(c_0_3333,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),one_one(X1)),one_one(X1))))
    | ~ linordered_semidom(X1) ),
    c_0_2371,
    [final] ).

cnf(c_0_3334,plain,
    ( X1 = X2
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    c_0_2372,
    [final] ).

cnf(c_0_3335,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),one_one(X1))))
    | ~ linordered_semidom(X1) ),
    c_0_2373,
    [final] ).

cnf(c_0_3336,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4))
    | ~ comm_semiring_1(X1) ),
    c_0_2374,
    [final] ).

cnf(c_0_3337,plain,
    ( hBOOL(hAPP(nat,bool,X3,X1))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,X3,X2))
    | ~ hBOOL(hAPP(nat,bool,X3,esk86_3(X3,X1,X2))) ),
    c_0_2375,
    [final] ).

cnf(c_0_3338,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ dense_linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),esk37_3(X1,X3,X2)),X3)) ),
    c_0_2376,
    [final] ).

cnf(c_0_3339,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X1,bool),nat,finite_card(X1),X2))) ),
    c_0_2377,
    [final] ).

cnf(c_0_3340,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    c_0_2378,
    [final] ).

cnf(c_0_3341,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
    c_0_2379,
    [final] ).

cnf(c_0_3342,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2))),
    c_0_2380,
    [final] ).

cnf(c_0_3343,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X1))),
    c_0_2381,
    [final] ).

cnf(c_0_3344,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | X1 = X2
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1)) ),
    c_0_2382,
    [final] ).

cnf(c_0_3345,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X3)),
    c_0_2383,
    [final] ).

cnf(c_0_3346,plain,
    ( hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,X1),X2))
    | hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,esk32_2(X1,X2)) != hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),esk32_2(X1,X2),X2) ),
    c_0_2384,
    [final] ).

cnf(c_0_3347,plain,
    ( hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
    | ~ hBOOL(hAPP(nat,bool,X1,X2))
    | ~ hBOOL(hAPP(nat,bool,X1,X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),esk81_2(X2,X1))) ),
    c_0_2385,
    [final] ).

cnf(c_0_3348,plain,
    ( hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
    | ~ hBOOL(hAPP(nat,bool,X1,X2))
    | ~ hBOOL(hAPP(nat,bool,X1,X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),esk79_2(X2,X1))) ),
    c_0_2386,
    [final] ).

cnf(c_0_3349,plain,
    ( hBOOL(hAPP(X1,bool,X2,X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X2))
    | ~ hBOOL(hAPP(X1,bool,X4,X3)) ),
    c_0_2387,
    [final] ).

cnf(c_0_3350,plain,
    ( hBOOL(hAPP(X1,bool,X2,X3))
    | ~ hBOOL(hAPP(X1,bool,X4,X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X2)) ),
    c_0_2388,
    [final] ).

cnf(c_0_3351,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk72_2(X1,X2)),X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
    c_0_2389,
    [final] ).

cnf(c_0_3352,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | X2 != hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X3)) ),
    c_0_2390,
    [final] ).

cnf(c_0_3353,plain,
    hAPP(X1,X2,hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X1,fun(X3,X2)),fun(fun(X1,X3),fun(X1,X2)),combs(X1,X3,X2),X4),X5),X6) = hAPP(X3,X2,hAPP(X1,fun(X3,X2),X4,X6),hAPP(X1,X3,X5,X6)),
    c_0_2391,
    [final] ).

cnf(c_0_3354,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk53_3(X1,X3,X2)),X2)) ),
    c_0_2392,
    [final] ).

cnf(c_0_3355,plain,
    ( X2 = hAPP(nat,nat,suc,X1)
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),esk93_2(X1,X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    c_0_2393,
    [final] ).

cnf(c_0_3356,plain,
    ( hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),esk87_2(X2,X1))) = X1
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1)) ),
    c_0_2394,
    [final] ).

cnf(c_0_3357,plain,
    ( hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),esk83_2(X2,X1))) = X1
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1)) ),
    c_0_2395,
    [final] ).

cnf(c_0_3358,plain,
    ( X1 = zero_zero(nat)
    | hAPP(nat,nat,suc,esk85_2(X1,X2)) = X1
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2))) ),
    c_0_2396,
    [final] ).

cnf(c_0_3359,plain,
    ( ti(X1,X2) = zero_zero(X1)
    | ~ ring_char_0(X1)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),ring_1_Ints(X1)))
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2) != zero_zero(X1) ),
    c_0_2397,
    [final] ).

cnf(c_0_3360,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ti(X1,X3) != ti(X1,X2) ),
    c_0_2398,
    [final] ).

cnf(c_0_3361,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | ti(X1,X3) != ti(X1,X4)
    | ~ order(X1) ),
    c_0_2399,
    [final] ).

cnf(c_0_3362,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ti(X1,X4) != ti(X1,X2)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
    | ~ order(X1) ),
    c_0_2400,
    [final] ).

cnf(c_0_3363,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ti(X1,X3) != ti(X1,X2) ),
    c_0_2401,
    [final] ).

cnf(c_0_3364,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | ti(X1,X3) != ti(X1,X4)
    | ~ order(X1) ),
    c_0_2402,
    [final] ).

cnf(c_0_3365,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X4) != ti(X1,X2)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
    | ~ order(X1) ),
    c_0_2403,
    [final] ).

cnf(c_0_3366,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X3) = ti(X1,X2)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ order(X1) ),
    c_0_2404,
    [final] ).

cnf(c_0_3367,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X2) = ti(X1,X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ order(X1) ),
    c_0_2405,
    [final] ).

cnf(c_0_3368,plain,
    ( ti(X1,X2) = ti(X1,X3)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ order(X1) ),
    c_0_2406,
    [final] ).

cnf(c_0_3369,plain,
    ( ti(X1,X2) = ti(X1,X3)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    c_0_2407,
    [final] ).

cnf(c_0_3370,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X3) = ti(X1,X2)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ order(X1) ),
    c_0_2408,
    [final] ).

cnf(c_0_3371,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X2) = ti(X1,X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ order(X1) ),
    c_0_2409,
    [final] ).

cnf(c_0_3372,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X2) = ti(X1,X3)
    | ~ linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    c_0_2410,
    [final] ).

cnf(c_0_3373,plain,
    ( ti(X1,X2) = ti(X1,X3)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    c_0_2411,
    [final] ).

cnf(c_0_3374,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X2) = ti(X1,X3)
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    c_0_2412,
    [final] ).

cnf(c_0_3375,plain,
    ( ti(X1,X2) = ti(X1,X3)
    | hAPP(X1,X4,X5,X2) != hAPP(X1,X4,X5,X3)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X4),fun(fun(X1,bool),bool),inj_on(X1,X4),X5),top_top(fun(X1,bool)))) ),
    c_0_2413,
    [final] ).

cnf(c_0_3376,plain,
    ( ti(X1,X4) = ti(X1,X5)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),top_top(fun(X1,bool))))
    | hAPP(X1,X2,X3,X4) != hAPP(X1,X2,X3,X5) ),
    c_0_2414,
    [final] ).

cnf(c_0_3377,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
    | X2 != X4
    | ~ ord(X1) ),
    c_0_2415,
    [final] ).

cnf(c_0_3378,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | X4 != X3
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | ~ ord(X1) ),
    c_0_2416,
    [final] ).

cnf(c_0_3379,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
    | X2 != X4
    | ~ ord(X1) ),
    c_0_2417,
    [final] ).

cnf(c_0_3380,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | X4 != X3
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | ~ ord(X1) ),
    c_0_2418,
    [final] ).

cnf(c_0_3381,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ preorder(X1) ),
    c_0_2419,
    [final] ).

cnf(c_0_3382,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    c_0_2420,
    [final] ).

cnf(c_0_3383,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ preorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    c_0_2421,
    [final] ).

cnf(c_0_3384,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    c_0_2422,
    [final] ).

cnf(c_0_3385,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2)))
    | X1 != X2 ),
    c_0_2423,
    [final] ).

cnf(c_0_3386,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1)) ),
    c_0_2424,
    [final] ).

cnf(c_0_3387,plain,
    hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X1),X2))),
    c_0_2425,
    [final] ).

cnf(c_0_3388,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),esk82_2(X1,X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    c_0_2426,
    [final] ).

cnf(c_0_3389,plain,
    hAPP(product_prod(X1,X2),X3,hAPP(fun(X1,fun(X2,X3)),fun(product_prod(X1,X2),X3),product_prod_rec(X1,X2,X3),X4),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X5),X6)) = hAPP(X2,X3,hAPP(X1,fun(X2,X3),X4,X5),X6),
    c_0_2427,
    [final] ).

cnf(c_0_3390,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | X1 = X2
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    c_0_2428,
    [final] ).

cnf(c_0_3391,plain,
    ( X1 = X2
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    c_0_2429,
    [final] ).

cnf(c_0_3392,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | X1 = X2
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    c_0_2430,
    [final] ).

cnf(c_0_3393,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    c_0_2431,
    [final] ).

cnf(c_0_3394,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    c_0_2432,
    [final] ).

cnf(c_0_3395,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    c_0_2433,
    [final] ).

cnf(c_0_3396,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    c_0_2434,
    [final] ).

cnf(c_0_3397,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    c_0_2435,
    [final] ).

cnf(c_0_3398,plain,
    ( X1 = zero_zero(nat)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,zero_zero(nat)))) ),
    c_0_2436,
    [final] ).

cnf(c_0_3399,plain,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),esk26_2(X1,X2)),arrow_2064824852le_Lin)) ),
    c_0_2437,
    [final] ).

cnf(c_0_3400,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X1,bool),nat,finite_card(X1),top_top(fun(X1,bool)))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool)))) ),
    c_0_2438,
    [final] ).

cnf(c_0_3401,plain,
    ( hAPP(X1,X2,X3,X4) = hAPP(X1,X2,X3,X5)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),top_top(fun(X1,bool))))
    | ti(X1,X4) != ti(X1,X5) ),
    c_0_2439,
    [final] ).

cnf(c_0_3402,plain,
    hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),esk66_0),arrow_2064824852le_Lin)),
    c_0_2440,
    [final] ).

cnf(c_0_3403,plain,
    hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),esk19_0),arrow_2064824852le_Lin)),
    c_0_2441,
    [final] ).

cnf(c_0_3404,plain,
    hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),esk18_0),arrow_2064824852le_Lin)),
    c_0_2442,
    [final] ).

cnf(c_0_3405,plain,
    hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),lba),arrow_2064824852le_Lin)),
    c_0_2443,
    [final] ).

cnf(c_0_3406,plain,
    hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),lab),arrow_2064824852le_Lin)),
    c_0_2444,
    [final] ).

cnf(c_0_3407,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2) = zero_zero(X1)
    | ~ ring_char_0(X1)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),ring_1_Ints(X1)))
    | ti(X1,X2) != zero_zero(X1) ),
    c_0_2445,
    [final] ).

cnf(c_0_3408,plain,
    ( hBOOL(hAPP(nat,bool,X1,X2))
    | ~ hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
    | ~ hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,suc,esk98_2(X2,X1)))) ),
    c_0_2446,
    [final] ).

cnf(c_0_3409,plain,
    ( hAPP(fun(sum_sum(X1,X2),bool),nat,finite_card(sum_sum(X1,X2)),hAPP(fun(X2,bool),fun(sum_sum(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X2,bool),fun(sum_sum(X1,X2),bool)),sum_Plus(X1,X2),X3),X4)) = zero_zero(nat)
    | hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    c_0_2447,
    [final] ).

cnf(c_0_3410,plain,
    ( hAPP(fun(sum_sum(X1,X2),bool),nat,finite_card(sum_sum(X1,X2)),hAPP(fun(X2,bool),fun(sum_sum(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X2,bool),fun(sum_sum(X1,X2),bool)),sum_Plus(X1,X2),X3),X4)) = zero_zero(nat)
    | hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4)) ),
    c_0_2448,
    [final] ).

cnf(c_0_3411,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),esk37_3(X1,X3,X2)),X2))
    | ~ dense_linorder(X1) ),
    c_0_2449,
    [final] ).

cnf(c_0_3412,plain,
    hAPP(X1,X2,hAPP(X3,fun(X1,X2),hAPP(fun(X1,fun(X3,X2)),fun(X3,fun(X1,X2)),combc(X1,X3,X2),X4),X5),X6) = hAPP(X3,X2,hAPP(X1,fun(X3,X2),X4,X6),X5),
    c_0_2450,
    [final] ).

cnf(c_0_3413,plain,
    hAPP(X1,X2,hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),combb(X3,X2,X1),X4),X5),X6) = hAPP(X3,X2,X4,hAPP(X1,X3,X5,X6)),
    c_0_2451,
    [final] ).

cnf(c_0_3414,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | ti(X1,esk70_4(X2,X1,X3,X4)) != ti(X1,esk69_4(X2,X1,X3,X4)) ),
    c_0_2452,
    [final] ).

cnf(c_0_3415,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | ti(X1,esk31_4(X1,X2,X3,X4)) != ti(X1,esk30_4(X1,X2,X3,X4)) ),
    c_0_2453,
    [final] ).

cnf(c_0_3416,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,X1)),X2) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),
    c_0_2454,
    [final] ).

cnf(c_0_3417,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | hAPP(X1,X2,X3,esk70_4(X2,X1,X3,X4)) = hAPP(X1,X2,X3,esk69_4(X2,X1,X3,X4)) ),
    c_0_2455,
    [final] ).

cnf(c_0_3418,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | hAPP(X1,X2,X3,esk31_4(X1,X2,X3,X4)) = hAPP(X1,X2,X3,esk30_4(X1,X2,X3,X4)) ),
    c_0_2456,
    [final] ).

cnf(c_0_3419,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),esk99_3(X1,X2,X3)))
    | ~ linordered_field(X1) ),
    c_0_2457,
    [final] ).

cnf(c_0_3420,plain,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3))
    | ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3) ),
    c_0_2458,
    [final] ).

cnf(c_0_3421,plain,
    ( hBOOL(hAPP(X1,bool,X2,X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X2)) ),
    c_0_2459,
    [final] ).

cnf(c_0_3422,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),esk82_2(X1,X2)) = X2
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    c_0_2460,
    [final] ).

cnf(c_0_3423,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),esk60_2(X2,X1)) = X1
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1)) ),
    c_0_2461,
    [final] ).

cnf(c_0_3424,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ linorder(X1)
    | ti(X1,X2) != ti(X1,X3) ),
    c_0_2462,
    [final] ).

cnf(c_0_3425,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ti(X1,X3) = ti(X1,X2)
    | ~ linordered_idom(X1) ),
    c_0_2463,
    [final] ).

cnf(c_0_3426,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ti(X1,X3) = ti(X1,X2)
    | ~ linorder(X1) ),
    c_0_2464,
    [final] ).

cnf(c_0_3427,plain,
    ( ti(X1,X2) = ti(X1,X3)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ linorder(X1) ),
    c_0_2465,
    [final] ).

cnf(c_0_3428,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X3) = ti(X1,X2)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ linorder(X1) ),
    c_0_2466,
    [final] ).

cnf(c_0_3429,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X3) = ti(X1,X2)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ linorder(X1) ),
    c_0_2467,
    [final] ).

cnf(c_0_3430,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ti(X1,X3) = ti(X1,X2)
    | ~ linorder(X1) ),
    c_0_2468,
    [final] ).

cnf(c_0_3431,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X3) = ti(X1,X2)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ linorder(X1) ),
    c_0_2469,
    [final] ).

cnf(c_0_3432,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ linorder(X1) ),
    c_0_2470,
    [final] ).

cnf(c_0_3433,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ linorder(X1) ),
    c_0_2471,
    [final] ).

cnf(c_0_3434,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ linorder(X1) ),
    c_0_2472,
    [final] ).

cnf(c_0_3435,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ linorder(X1) ),
    c_0_2473,
    [final] ).

cnf(c_0_3436,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ linorder(X1) ),
    c_0_2474,
    [final] ).

cnf(c_0_3437,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ linorder(X1) ),
    c_0_2475,
    [final] ).

cnf(c_0_3438,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ linorder(X1) ),
    c_0_2476,
    [final] ).

cnf(c_0_3439,plain,
    ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X1))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk78_2(X2,X1)),X2)) ),
    c_0_2477,
    [final] ).

cnf(c_0_3440,plain,
    ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X1))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk76_2(X1,X2)),X2)) ),
    c_0_2478,
    [final] ).

cnf(c_0_3441,plain,
    ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X1))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),esk74_2(X1,X2)),X2)) ),
    c_0_2479,
    [final] ).

cnf(c_0_3442,plain,
    ( hBOOL(hAPP(fun(sum_sum(X1,X2),bool),bool,finite_finite_1(sum_sum(X1,X2)),top_top(fun(sum_sum(X1,X2),bool))))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),top_top(fun(X2,bool))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool)))) ),
    c_0_2480,
    [final] ).

cnf(c_0_3443,plain,
    ( hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,finite_finite_1(product_prod(X1,X2)),top_top(fun(product_prod(X1,X2),bool))))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),top_top(fun(X2,bool))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool)))) ),
    c_0_2481,
    [final] ).

cnf(c_0_3444,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1))
    | X2 = X1 ),
    c_0_2482,
    [final] ).

cnf(c_0_3445,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1))
    | X2 = X1 ),
    c_0_2483,
    [final] ).

cnf(c_0_3446,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1)) ),
    c_0_2484,
    [final] ).

cnf(c_0_3447,plain,
    ( ti(X2,X3) = ti(X2,X5)
    | hAPP(X1,product_prod(X2,X1),hAPP(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),X3),X4) != hAPP(X1,product_prod(X2,X1),hAPP(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),X5),X6) ),
    c_0_2485,
    [final] ).

cnf(c_0_3448,plain,
    ( ti(X1,X4) = ti(X1,X6)
    | hAPP(X1,product_prod(X2,X1),hAPP(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),X3),X4) != hAPP(X1,product_prod(X2,X1),hAPP(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),X5),X6) ),
    c_0_2486,
    [final] ).

cnf(c_0_3449,plain,
    ( ti(X2,X3) = ti(X2,X5)
    | hAPP(X1,product_prod(X2,X1),hAPP(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),X3),X4) != hAPP(X1,product_prod(X2,X1),hAPP(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),X5),X6) ),
    c_0_2487,
    [final] ).

cnf(c_0_3450,plain,
    ( ti(X1,X4) = ti(X1,X6)
    | hAPP(X1,product_prod(X2,X1),hAPP(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),X3),X4) != hAPP(X1,product_prod(X2,X1),hAPP(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),X5),X6) ),
    c_0_2488,
    [final] ).

cnf(c_0_3451,plain,
    ( hAPP(fun(X1,bool),nat,finite_card(X1),X2) = zero_zero(nat)
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),esk80_2(X1,X2)),X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
    c_0_2489,
    [final] ).

cnf(c_0_3452,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),hAPP(nat,nat,suc,X2)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),
    c_0_2490,
    [final] ).

cnf(c_0_3453,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,X1)),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),hAPP(nat,nat,suc,X2)),
    c_0_2491,
    [final] ).

cnf(c_0_3454,plain,
    ( X2 = hAPP(nat,nat,suc,X1)
    | hAPP(nat,nat,suc,esk93_2(X1,X2)) = X2
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    c_0_2492,
    [final] ).

cnf(c_0_3455,plain,
    ( hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),esk81_2(X2,X1)),X2))
    | ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
    c_0_2493,
    [final] ).

cnf(c_0_3456,plain,
    ( hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk79_2(X2,X1)),X2))
    | ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
    c_0_2494,
    [final] ).

cnf(c_0_3457,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,suc,X2)))
    | X1 != hAPP(nat,nat,suc,X2) ),
    c_0_2495,
    [final] ).

cnf(c_0_3458,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool))))
    | hAPP(fun(X2,bool),nat,finite_card(X2),top_top(fun(X2,bool))) = hAPP(nat,nat,suc,zero_zero(nat))
    | ~ hBOOL(hAPP(fun(fun(X1,X2),bool),bool,finite_finite_1(fun(X1,X2)),top_top(fun(fun(X1,X2),bool)))) ),
    c_0_2496,
    [final] ).

cnf(c_0_3459,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),top_top(fun(X1,bool))))
    | hAPP(X1,X2,X3,esk36_3(X1,X2,X3)) = hAPP(X1,X2,X3,esk35_3(X1,X2,X3)) ),
    c_0_2497,
    [final] ).

cnf(c_0_3460,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk28_0),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool))))),
    c_0_2498,
    [final] ).

cnf(c_0_3461,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),esk27_0),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool))))),
    c_0_2499,
    [final] ).

cnf(c_0_3462,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),n),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool))))),
    c_0_2500,
    [final] ).

cnf(c_0_3463,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | X2 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X3) ),
    c_0_2501,
    [final] ).

cnf(c_0_3464,plain,
    ( hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
    | hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,suc,esk97_1(X1))))
    | ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
    c_0_2502,
    [final] ).

cnf(c_0_3465,plain,
    ( hAPP(nat,nat,suc,esk88_1(X1)) = X1
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
    c_0_2503,
    [final] ).

cnf(c_0_3466,plain,
    ( hAPP(nat,nat,suc,esk84_1(X1)) = X1
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
    c_0_2504,
    [final] ).

cnf(c_0_3467,plain,
    hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool)))) = hAPP(fun(arrow_660593299e_indi,bool),fun(nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(fun(arrow_660593299e_indi,bool),fun(nat,bool)),image(arrow_660593299e_indi,nat),esk100_0),top_top(fun(arrow_660593299e_indi,bool))),
    c_0_2505,
    [final] ).

cnf(c_0_3468,plain,
    hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool)))) = hAPP(fun(arrow_660593299e_indi,bool),fun(nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(fun(arrow_660593299e_indi,bool),fun(nat,bool)),image(arrow_660593299e_indi,nat),h),top_top(fun(arrow_660593299e_indi,bool))),
    c_0_2506,
    [final] ).

cnf(c_0_3469,plain,
    hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X3),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),top_top(fun(X2,bool)))) = top_top(fun(fun(X1,X2),bool)),
    c_0_2507,
    [final] ).

cnf(c_0_3470,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,X3,X2)) ),
    c_0_2508,
    [final] ).

cnf(c_0_3471,plain,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),zero_zero(X1)))
    | ~ linordered_semidom(X1) ),
    c_0_2509,
    [final] ).

cnf(c_0_3472,plain,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),one_one(X1)),zero_zero(X1)))
    | ~ linordered_semidom(X1) ),
    c_0_2510,
    [final] ).

cnf(c_0_3473,plain,
    ( ti(X1,X2) = top_top(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),top_top(X1)),X2))
    | ~ top(X1) ),
    c_0_2511,
    [final] ).

cnf(c_0_3474,plain,
    ( ti(X1,X2) = top_top(X1)
    | ~ top(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),top_top(X1)),X2)) ),
    c_0_2512,
    [final] ).

cnf(c_0_3475,plain,
    ( ti(X1,X2) = ti(X1,X3)
    | ~ cancel_semigroup_add(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X2) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3) ),
    c_0_2513,
    [final] ).

cnf(c_0_3476,plain,
    ( ti(X1,X2) = ti(X1,X3)
    | ~ cancel_semigroup_add(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4) ),
    c_0_2514,
    [final] ).

cnf(c_0_3477,plain,
    ( ti(X1,X2) = ti(X1,X3)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X2) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)
    | ~ cancel_semigroup_add(X1) ),
    c_0_2515,
    [final] ).

cnf(c_0_3478,plain,
    ( ti(X1,X2) = ti(X1,X3)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X2) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)
    | ~ cancel146912293up_add(X1) ),
    c_0_2516,
    [final] ).

cnf(c_0_3479,plain,
    ( ti(X1,X2) = ti(X1,X3)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)
    | ~ cancel_semigroup_add(X1) ),
    c_0_2517,
    [final] ).

cnf(c_0_3480,plain,
    ( ~ top(X1)
    | ti(X1,X2) != top_top(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),top_top(X1))) ),
    c_0_2518,
    [final] ).

cnf(c_0_3481,plain,
    ( ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X2) != ti(X1,X3) ),
    c_0_2519,
    [final] ).

cnf(c_0_3482,plain,
    ( ~ linorder(X1)
    | ti(X1,X2) != ti(X1,X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    c_0_2520,
    [final] ).

cnf(c_0_3483,plain,
    ( ~ linorder(X1)
    | ti(X1,X2) != ti(X1,X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2)) ),
    c_0_2521,
    [final] ).

cnf(c_0_3484,plain,
    ( ~ linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X2) != ti(X1,X3) ),
    c_0_2522,
    [final] ).

cnf(c_0_3485,plain,
    ( ti(X1,X2) != ti(X1,X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ order(X1) ),
    c_0_2523,
    [final] ).

cnf(c_0_3486,plain,
    ( ti(X1,X2) != ti(X1,X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ order(X1) ),
    c_0_2524,
    [final] ).

cnf(c_0_3487,plain,
    ( ti(X1,X2) != ti(X1,X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ order(X1) ),
    c_0_2525,
    [final] ).

cnf(c_0_3488,plain,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),top_top(X1)),X2))
    | ~ top(X1) ),
    c_0_2526,
    [final] ).

cnf(c_0_3489,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,zero_zero(nat))))
    | X1 != zero_zero(nat) ),
    c_0_2527,
    [final] ).

cnf(c_0_3490,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,X1))),
    c_0_2528,
    [final] ).

cnf(c_0_3491,plain,
    ( ti(X1,X2) = ti(X1,X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),fequal(X1),X2),X3)) ),
    c_0_2529,
    [final] ).

cnf(c_0_3492,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2)))
    | X1 != zero_zero(nat) ),
    c_0_2530,
    [final] ).

cnf(c_0_3493,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2)))
    | X1 != X2 ),
    c_0_2531,
    [final] ).

cnf(c_0_3494,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X1))),
    c_0_2532,
    [final] ).

cnf(c_0_3495,plain,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X2))
    | ~ preorder(X1) ),
    c_0_2533,
    [final] ).

cnf(c_0_3496,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),top_top(fun(X1,bool))))
    | ti(X1,esk36_3(X1,X2,X3)) != ti(X1,esk35_3(X1,X2,X3)) ),
    c_0_2534,
    [final] ).

cnf(c_0_3497,plain,
    ( X1 != zero_zero(nat)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
    c_0_2535,
    [final] ).

cnf(c_0_3498,plain,
    ( X1 = zero_zero(nat)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),zero_zero(nat))) ),
    c_0_2536,
    [final] ).

cnf(c_0_3499,plain,
    ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),zero_zero(nat))),
    c_0_2537,
    [final] ).

cnf(c_0_3500,plain,
    ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),zero_zero(nat))),
    c_0_2538,
    [final] ).

cnf(c_0_3501,plain,
    ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),zero_zero(nat))),
    c_0_2539,
    [final] ).

cnf(c_0_3502,plain,
    ( X1 != zero_zero(nat)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1)) ),
    c_0_2540,
    [final] ).

cnf(c_0_3503,plain,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | X1 != X2 ),
    c_0_2541,
    [final] ).

cnf(c_0_3504,plain,
    ( X1 != X2
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    c_0_2542,
    [final] ).

cnf(c_0_3505,plain,
    ( X1 != X2
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1)) ),
    c_0_2543,
    [final] ).

cnf(c_0_3506,plain,
    ( X1 != X2
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    c_0_2544,
    [final] ).

cnf(c_0_3507,plain,
    ( X1 != X2
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1)) ),
    c_0_2545,
    [final] ).

cnf(c_0_3508,plain,
    ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X1)),
    c_0_2546,
    [final] ).

cnf(c_0_3509,plain,
    ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X1)),
    c_0_2547,
    [final] ).

cnf(c_0_3510,plain,
    ( X1 = X2
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X3) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3) ),
    c_0_2548,
    [final] ).

cnf(c_0_3511,plain,
    ( X1 = X2
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X1) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X2) ),
    c_0_2549,
    [final] ).

cnf(c_0_3512,plain,
    ( hBOOL(X1)
    | hBOOL(X2)
    | ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X2),X1)) ),
    c_0_2550,
    [final] ).

cnf(c_0_3513,plain,
    ( hBOOL(X1)
    | ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X2),X1)) ),
    c_0_2551,
    [final] ).

cnf(c_0_3514,plain,
    ( hBOOL(X1)
    | ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X1),X2)) ),
    c_0_2552,
    [final] ).

cnf(c_0_3515,plain,
    ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X1))
    | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),esk78_2(X2,X1)),X1)) ),
    c_0_2553,
    [final] ).

cnf(c_0_3516,plain,
    ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X1))
    | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),esk76_2(X1,X2)),X1)) ),
    c_0_2554,
    [final] ).

cnf(c_0_3517,plain,
    ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X1))
    | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),esk74_2(X1,X2)),X1)) ),
    c_0_2555,
    [final] ).

cnf(c_0_3518,plain,
    ( ti(fun(X1,X2),X3) = ti(fun(X1,X2),X4)
    | hAPP(X1,X2,X3,esk20_4(X1,X2,X3,X4)) != hAPP(X1,X2,X4,esk20_4(X1,X2,X3,X4)) ),
    c_0_2556,
    [final] ).

cnf(c_0_3519,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool))))
    | ~ hBOOL(hAPP(fun(fun(X2,X1),bool),bool,finite_finite_1(fun(X2,X1)),top_top(fun(fun(X2,X1),bool)))) ),
    c_0_2557,
    [final] ).

cnf(c_0_3520,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool))))
    | ~ hBOOL(hAPP(fun(sum_sum(X1,X2),bool),bool,finite_finite_1(sum_sum(X1,X2)),top_top(fun(sum_sum(X1,X2),bool)))) ),
    c_0_2558,
    [final] ).

cnf(c_0_3521,plain,
    ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),top_top(fun(X2,bool))))
    | ~ hBOOL(hAPP(fun(sum_sum(X1,X2),bool),bool,finite_finite_1(sum_sum(X1,X2)),top_top(fun(sum_sum(X1,X2),bool)))) ),
    c_0_2559,
    [final] ).

cnf(c_0_3522,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3) ),
    c_0_2560,
    [final] ).

cnf(c_0_3523,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X2))
    | ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3) ),
    c_0_2561,
    [final] ).

cnf(c_0_3524,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3) ),
    c_0_2562,
    [final] ).

cnf(c_0_3525,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ti(fun(X1,bool),X3) != ti(fun(X1,bool),X2) ),
    c_0_2563,
    [final] ).

cnf(c_0_3526,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3) ),
    c_0_2564,
    [final] ).

cnf(c_0_3527,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X2))
    | ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3) ),
    c_0_2565,
    [final] ).

cnf(c_0_3528,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3) ),
    c_0_2566,
    [final] ).

cnf(c_0_3529,plain,
    hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),top_top(fun(X1,bool)))),
    c_0_2567,
    [final] ).

cnf(c_0_3530,plain,
    hAPP(X1,X1,hAPP(X1,fun(X1,X1),hAPP(bool,fun(X1,fun(X1,X1)),if(X1),fFalse),X2),X3) = ti(X1,X3),
    c_0_2568,
    [final] ).

cnf(c_0_3531,plain,
    hAPP(X1,X1,hAPP(X1,fun(X1,X1),hAPP(bool,fun(X1,fun(X1,X1)),if(X1),fTrue),X2),X3) = ti(X1,X2),
    c_0_2569,
    [final] ).

cnf(c_0_3532,plain,
    ( X1 = hAPP(nat,nat,suc,zero_zero(nat))
    | X2 = hAPP(nat,nat,suc,zero_zero(nat))
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) != hAPP(nat,nat,suc,zero_zero(nat)) ),
    c_0_2570,
    [final] ).

cnf(c_0_3533,plain,
    ( X1 = hAPP(nat,nat,suc,zero_zero(nat))
    | X2 = hAPP(nat,nat,suc,zero_zero(nat))
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) != hAPP(nat,nat,suc,zero_zero(nat)) ),
    c_0_2571,
    [final] ).

cnf(c_0_3534,plain,
    hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X2)),
    c_0_2572,
    [final] ).

cnf(c_0_3535,plain,
    ( hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
    | ~ hBOOL(hAPP(nat,bool,X1,X2))
    | ~ hBOOL(hAPP(nat,bool,X1,esk97_1(X1))) ),
    c_0_2573,
    [final] ).

cnf(c_0_3536,plain,
    ( ti(fun(X1,bool),X2) = top_top(fun(X1,bool))
    | hAPP(fun(X1,bool),nat,finite_card(X1),X2) != hAPP(fun(X1,bool),nat,finite_card(X1),top_top(fun(X1,bool)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool)))) ),
    c_0_2574,
    [final] ).

cnf(c_0_3537,plain,
    ( hAPP(X1,product_prod(X2,X1),hAPP(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),X3),X4) = hAPP(X1,product_prod(X2,X1),hAPP(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),X5),X6)
    | ti(X1,X4) != ti(X1,X6)
    | ti(X2,X3) != ti(X2,X5) ),
    c_0_2575,
    [final] ).

cnf(c_0_3538,plain,
    hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),combi(X1)),X2)),
    c_0_2576,
    [final] ).

cnf(c_0_3539,plain,
    hBOOL(hAPP(fun(arrow_660593299e_indi,bool),bool,hAPP(fun(arrow_660593299e_indi,nat),fun(fun(arrow_660593299e_indi,bool),bool),inj_on(arrow_660593299e_indi,nat),esk100_0),top_top(fun(arrow_660593299e_indi,bool)))),
    c_0_2577,
    [final] ).

cnf(c_0_3540,plain,
    hBOOL(hAPP(fun(arrow_660593299e_indi,bool),bool,hAPP(fun(arrow_660593299e_indi,nat),fun(fun(arrow_660593299e_indi,bool),bool),inj_on(arrow_660593299e_indi,nat),h),top_top(fun(arrow_660593299e_indi,bool)))),
    c_0_2578,
    [final] ).

cnf(c_0_3541,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
    | X1 != hAPP(nat,nat,suc,X2) ),
    c_0_2579,
    [final] ).

cnf(c_0_3542,plain,
    ti(fun(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool)))),finite908156982e_idem(X1,X2)) = finite908156982e_idem(X1,X2),
    c_0_2580,
    [final] ).

cnf(c_0_3543,plain,
    hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),top_top(fun(X1,bool)))),
    c_0_2581,
    [final] ).

cnf(c_0_3544,plain,
    hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),top_top(fun(X1,bool)))),
    c_0_2582,
    [final] ).

cnf(c_0_3545,plain,
    hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,nat),fun(fun(nat,bool),bool),inj_on(nat,nat),suc),X1)),
    c_0_2583,
    [final] ).

cnf(c_0_3546,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),one_one(X1)),ring_1_Ints(X1)))
    | ~ ring_1(X1) ),
    c_0_2584,
    [final] ).

cnf(c_0_3547,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),zero_zero(X1)),ring_1_Ints(X1)))
    | ~ ring_1(X1) ),
    c_0_2585,
    [final] ).

cnf(c_0_3548,plain,
    ( X1 = hAPP(nat,nat,suc,zero_zero(nat))
    | X1 = zero_zero(nat)
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) != hAPP(nat,nat,suc,zero_zero(nat)) ),
    c_0_2586,
    [final] ).

cnf(c_0_3549,plain,
    ( X2 = zero_zero(nat)
    | X2 = hAPP(nat,nat,suc,zero_zero(nat))
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) != hAPP(nat,nat,suc,zero_zero(nat)) ),
    c_0_2587,
    [final] ).

cnf(c_0_3550,plain,
    ( X1 = hAPP(nat,nat,suc,zero_zero(nat))
    | X1 = zero_zero(nat)
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) != hAPP(nat,nat,suc,zero_zero(nat)) ),
    c_0_2588,
    [final] ).

cnf(c_0_3551,plain,
    ( X2 = zero_zero(nat)
    | X2 = hAPP(nat,nat,suc,zero_zero(nat))
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) != hAPP(nat,nat,suc,zero_zero(nat)) ),
    c_0_2589,
    [final] ).

cnf(c_0_3552,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool))))
    | ~ hBOOL(hAPP(fun(option(X1),bool),bool,finite_finite_1(option(X1)),top_top(fun(option(X1),bool)))) ),
    c_0_2590,
    [final] ).

cnf(c_0_3553,plain,
    ( hBOOL(hAPP(nat,bool,X1,X2))
    | hBOOL(hAPP(nat,bool,X1,esk98_2(X2,X1)))
    | ~ hBOOL(hAPP(nat,bool,X1,zero_zero(nat))) ),
    c_0_2591,
    [final] ).

cnf(c_0_3554,plain,
    ( hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
    | hBOOL(hAPP(nat,bool,X1,esk81_2(X2,X1)))
    | ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
    c_0_2592,
    [final] ).

cnf(c_0_3555,plain,
    ( hBOOL(hAPP(fun(option(X1),bool),bool,finite_finite_1(option(X1)),top_top(fun(option(X1),bool))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool)))) ),
    c_0_2593,
    [final] ).

cnf(c_0_3556,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)
    | ~ cancel_semigroup_add(X1)
    | ti(X1,X3) != ti(X1,X4) ),
    c_0_2594,
    [final] ).

cnf(c_0_3557,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)
    | ~ cancel_semigroup_add(X1)
    | ti(X1,X2) != ti(X1,X4) ),
    c_0_2595,
    [final] ).

cnf(c_0_3558,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),top_top(X1)),X2))
    | ~ top(X1)
    | ti(X1,X2) != top_top(X1) ),
    c_0_2596,
    [final] ).

cnf(c_0_3559,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ order(X1)
    | ti(X1,X2) != ti(X1,X3) ),
    c_0_2597,
    [final] ).

cnf(c_0_3560,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ order(X1)
    | ti(X1,X2) != ti(X1,X3) ),
    c_0_2598,
    [final] ).

cnf(c_0_3561,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ order(X1)
    | ti(X1,X2) != ti(X1,X3) ),
    c_0_2599,
    [final] ).

cnf(c_0_3562,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),fequal(X1),X2),X3))
    | ti(X1,X2) != ti(X1,X3) ),
    c_0_2600,
    [final] ).

cnf(c_0_3563,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),one_one(X1)))
    | ~ linordered_semidom(X1) ),
    c_0_2601,
    [final] ).

cnf(c_0_3564,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),one_one(X1)))
    | ~ linordered_semidom(X1) ),
    c_0_2602,
    [final] ).

cnf(c_0_3565,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),top_top(X1)))
    | ti(X1,X2) = top_top(X1)
    | ~ top(X1) ),
    c_0_2603,
    [final] ).

cnf(c_0_3566,plain,
    ( X2 = zero_zero(nat)
    | X1 = zero_zero(nat)
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) != hAPP(nat,nat,suc,zero_zero(nat)) ),
    c_0_2604,
    [final] ).

cnf(c_0_3567,plain,
    ( X2 = zero_zero(nat)
    | X1 = zero_zero(nat)
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) != hAPP(nat,nat,suc,zero_zero(nat)) ),
    c_0_2605,
    [final] ).

cnf(c_0_3568,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X2)
    | ~ comm_semiring_1(X1) ),
    c_0_2606,
    [final] ).

cnf(c_0_3569,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),top_top(X1)))
    | ~ top(X1) ),
    c_0_2607,
    [final] ).

cnf(c_0_3570,plain,
    hAPP(fun(X1,bool),fun(sum_sum(X2,X1),bool),hAPP(fun(X2,bool),fun(fun(X1,bool),fun(sum_sum(X2,X1),bool)),sum_Plus(X2,X1),top_top(fun(X2,bool))),top_top(fun(X1,bool))) = top_top(fun(sum_sum(X2,X1),bool)),
    c_0_2608,
    [final] ).

cnf(c_0_3571,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | X2 != X3
    | ~ preorder(X1) ),
    c_0_2609,
    [final] ).

cnf(c_0_3572,plain,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X2))
    | ~ preorder(X1) ),
    c_0_2610,
    [final] ).

cnf(c_0_3573,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
    | X1 = zero_zero(nat) ),
    c_0_2611,
    [final] ).

cnf(c_0_3574,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
    | X1 = zero_zero(nat) ),
    c_0_2612,
    [final] ).

cnf(c_0_3575,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),X1)),
    c_0_2613,
    [final] ).

cnf(c_0_3576,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),X1)),
    c_0_2614,
    [final] ).

cnf(c_0_3577,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),zero_zero(nat)))
    | X1 != zero_zero(nat) ),
    c_0_2615,
    [final] ).

cnf(c_0_3578,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | X1 != X2 ),
    c_0_2616,
    [final] ).

cnf(c_0_3579,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | X1 != X2 ),
    c_0_2617,
    [final] ).

cnf(c_0_3580,plain,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | X1 != X2 ),
    c_0_2618,
    [final] ).

cnf(c_0_3581,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X2)
    | X1 != X3 ),
    c_0_2619,
    [final] ).

cnf(c_0_3582,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X3)
    | X2 != X3 ),
    c_0_2620,
    [final] ).

cnf(c_0_3583,plain,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X1)),
    c_0_2621,
    [final] ).

cnf(c_0_3584,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X1),
    c_0_2622,
    [final] ).

cnf(c_0_3585,plain,
    ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X1),X2))
    | ~ hBOOL(X2)
    | ~ hBOOL(X1) ),
    c_0_2623,
    [final] ).

cnf(c_0_3586,plain,
    ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X1),X2))
    | ~ hBOOL(X2) ),
    c_0_2624,
    [final] ).

cnf(c_0_3587,plain,
    ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X1),X2))
    | ~ hBOOL(X1) ),
    c_0_2625,
    [final] ).

cnf(c_0_3588,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) = hAPP(nat,nat,suc,zero_zero(nat))
    | X2 != zero_zero(nat)
    | X1 != hAPP(nat,nat,suc,zero_zero(nat)) ),
    c_0_2626,
    [final] ).

cnf(c_0_3589,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) = hAPP(nat,nat,suc,zero_zero(nat))
    | X2 != hAPP(nat,nat,suc,zero_zero(nat))
    | X1 != zero_zero(nat) ),
    c_0_2627,
    [final] ).

cnf(c_0_3590,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) = hAPP(nat,nat,suc,zero_zero(nat))
    | X2 != zero_zero(nat)
    | X1 != hAPP(nat,nat,suc,zero_zero(nat)) ),
    c_0_2628,
    [final] ).

cnf(c_0_3591,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) = hAPP(nat,nat,suc,zero_zero(nat))
    | X2 != hAPP(nat,nat,suc,zero_zero(nat))
    | X1 != zero_zero(nat) ),
    c_0_2629,
    [final] ).

cnf(c_0_3592,plain,
    hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,f)),
    c_0_2630,
    [final] ).

cnf(c_0_3593,plain,
    hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,f)),
    c_0_2631,
    [final] ).

cnf(c_0_3594,plain,
    ( ti(X1,X2) = zero_zero(X1)
    | ~ semiri456707255roduct(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X2) != ti(X1,X3) ),
    c_0_2632,
    [final] ).

cnf(c_0_3595,plain,
    ( ti(X1,X2) = zero_zero(X1)
    | ~ linord219039673up_add(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2) != zero_zero(X1) ),
    c_0_2633,
    [final] ).

cnf(c_0_3596,plain,
    ( ti(X1,X2) = zero_zero(X1)
    | ~ linord219039673up_add(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2) != zero_zero(X1) ),
    c_0_2634,
    [final] ).

cnf(c_0_3597,plain,
    ( X1 = zero_zero(nat)
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) != zero_zero(nat) ),
    c_0_2635,
    [final] ).

cnf(c_0_3598,plain,
    ( X2 = zero_zero(nat)
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) != zero_zero(nat) ),
    c_0_2636,
    [final] ).

cnf(c_0_3599,plain,
    ( X1 = zero_zero(nat)
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X1) != X2 ),
    c_0_2637,
    [final] ).

cnf(c_0_3600,plain,
    hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),combi(X1)),X2) = ti(fun(X1,bool),X2),
    c_0_2638,
    [final] ).

cnf(c_0_3601,plain,
    ( hAPP(fun(X1,bool),nat,finite_card(X1),X2) = zero_zero(nat)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | zero_zero(nat) != one_one(nat) ),
    c_0_2639,
    [final] ).

cnf(c_0_3602,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),X1) = hAPP(nat,nat,suc,X1),
    c_0_2640,
    [final] ).

cnf(c_0_3603,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),one_one(nat)) = hAPP(nat,nat,suc,X1),
    c_0_2641,
    [final] ).

cnf(c_0_3604,plain,
    hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)) = hAPP(nat,fun(nat,bool),ord_less(nat),X1),
    c_0_2642,
    [final] ).

cnf(c_0_3605,plain,
    ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),top_top(fun(nat,bool)))),
    c_0_2643,
    [final] ).

cnf(c_0_3606,plain,
    ti(fun(fun(nat,fun(nat,nat)),fun(fun(X1,nat),fun(nat,fun(fun(X1,bool),nat)))),finite_fold_image(nat,X1)) = finite_fold_image(nat,X1),
    c_0_2644,
    [final] ).

cnf(c_0_3607,plain,
    ti(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool)),arrow_218898985ctator) = arrow_218898985ctator,
    c_0_2645,
    [final] ).

cnf(c_0_3608,plain,
    ti(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),arrow_831799591nimity) = arrow_831799591nimity,
    c_0_2646,
    [final] ).

cnf(c_0_3609,plain,
    ti(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),arrow_2037941124le_IIA) = arrow_2037941124le_IIA,
    c_0_2647,
    [final] ).

cnf(c_0_3610,plain,
    hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(bool,fun(X1,bool),combk(bool,X1),fTrue)) = top_top(fun(X1,bool)),
    c_0_2648,
    [final] ).

cnf(c_0_3611,plain,
    hAPP(X1,X2,hAPP(X2,fun(X1,X2),combk(X2,X1),X3),X4) = ti(X2,X3),
    c_0_2649,
    [final] ).

cnf(c_0_3612,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) = ti(X1,X2)
    | ~ semiri456707255roduct(X1)
    | ti(X1,X3) != zero_zero(X1) ),
    c_0_2650,
    [final] ).

cnf(c_0_3613,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2) = zero_zero(X1)
    | ~ linord219039673up_add(X1)
    | ti(X1,X2) != zero_zero(X1) ),
    c_0_2651,
    [final] ).

cnf(c_0_3614,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2) = zero_zero(X1)
    | ~ linord219039673up_add(X1)
    | ti(X1,X2) != zero_zero(X1) ),
    c_0_2652,
    [final] ).

cnf(c_0_3615,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),zero_zero(X1)),X2) = ti(X1,X2)
    | ~ comm_semiring_1(X1) ),
    c_0_2653,
    [final] ).

cnf(c_0_3616,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),zero_zero(X1)),X2) = ti(X1,X2)
    | ~ monoid_add(X1) ),
    c_0_2654,
    [final] ).

cnf(c_0_3617,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),zero_zero(X1)),X2) = ti(X1,X2)
    | ~ comm_monoid_add(X1) ),
    c_0_2655,
    [final] ).

cnf(c_0_3618,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),zero_zero(X1)) = ti(X1,X2)
    | ~ comm_semiring_1(X1) ),
    c_0_2656,
    [final] ).

cnf(c_0_3619,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),zero_zero(X1)) = ti(X1,X2)
    | ~ monoid_add(X1) ),
    c_0_2657,
    [final] ).

cnf(c_0_3620,plain,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),zero_zero(X1)) = ti(X1,X2)
    | ~ comm_monoid_add(X1) ),
    c_0_2658,
    [final] ).

cnf(c_0_3621,plain,
    ( hAPP(fun(X1,bool),nat,finite_card(X1),X2) = zero_zero(nat)
    | hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
    c_0_2659,
    [final] ).

cnf(c_0_3622,plain,
    ( hAPP(fun(X1,bool),nat,finite_card(X1),X2) = zero_zero(nat)
    | hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
    c_0_2660,
    [final] ).

cnf(c_0_3623,plain,
    ti(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),arrow_1322701812_below) = arrow_1322701812_below,
    c_0_2661,
    [final] ).

cnf(c_0_3624,plain,
    ti(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),arrow_14103264_above) = arrow_14103264_above,
    c_0_2662,
    [final] ).

cnf(c_0_3625,plain,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) = zero_zero(nat)
    | X2 != zero_zero(nat)
    | X1 != zero_zero(nat) ),
    c_0_2663,
    [final] ).

cnf(c_0_3626,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),X1) = X1,
    c_0_2664,
    [final] ).

cnf(c_0_3627,plain,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),zero_zero(nat)) = X1,
    c_0_2665,
    [final] ).

cnf(c_0_3628,plain,
    ( ~ hBOOL(X1)
    | ~ hBOOL(hAPP(bool,bool,fNot,X1)) ),
    c_0_2666,
    [final] ).

cnf(c_0_3629,plain,
    ( X1 = X2
    | hAPP(nat,nat,suc,X1) != hAPP(nat,nat,suc,X2) ),
    c_0_2667,
    [final] ).

cnf(c_0_3630,plain,
    ( X1 = X2
    | hAPP(nat,nat,suc,X1) != hAPP(nat,nat,suc,X2) ),
    c_0_2668,
    [final] ).

cnf(c_0_3631,plain,
    ti(fun(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool))),pi(X1,X2)) = pi(X1,X2),
    c_0_2669,
    [final] ).

cnf(c_0_3632,plain,
    ti(X1,hAPP(X2,X1,X3,X4)) = hAPP(X2,X1,X3,X4),
    c_0_2670,
    [final] ).

cnf(c_0_3633,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool))))
    | ~ finite_finite(X1) ),
    c_0_2671,
    [final] ).

cnf(c_0_3634,plain,
    hBOOL(hAPP(fun(arrow_660593299e_indi,bool),bool,finite_finite_1(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool)))),
    c_0_2672,
    [final] ).

cnf(c_0_3635,plain,
    ti(fun(fun(X1,fun(X2,X3)),fun(fun(X1,X2),fun(X1,X3))),combs(X1,X2,X3)) = combs(X1,X2,X3),
    c_0_2673,
    [final] ).

cnf(c_0_3636,plain,
    hBOOL(hAPP(X1,bool,top_top(fun(X1,bool)),X2)),
    c_0_2674,
    [final] ).

cnf(c_0_3637,plain,
    hAPP(X1,X2,ti(fun(X1,X2),X3),X4) = hAPP(X1,X2,X3,X4),
    c_0_2675,
    [final] ).

cnf(c_0_3638,plain,
    ti(fun(fun(X1,bool),fun(fun(X2,bool),fun(sum_sum(X1,X2),bool))),sum_Plus(X1,X2)) = sum_Plus(X1,X2),
    c_0_2676,
    [final] ).

cnf(c_0_3639,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ finite_finite(X1) ),
    c_0_2677,
    [final] ).

cnf(c_0_3640,plain,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ finite_finite(X1) ),
    c_0_2678,
    [final] ).

cnf(c_0_3641,plain,
    hAPP(X1,X2,X3,ti(X1,X4)) = hAPP(X1,X2,X3,X4),
    c_0_2679,
    [final] ).

cnf(c_0_3642,plain,
    ti(fun(fun(X1,fun(X2,X3)),fun(product_prod(X1,X2),X3)),product_prod_rec(X1,X2,X3)) = product_prod_rec(X1,X2,X3),
    c_0_2680,
    [final] ).

cnf(c_0_3643,plain,
    ti(fun(fun(X1,fun(X2,X3)),fun(X2,fun(X1,X3))),combc(X1,X2,X3)) = combc(X1,X2,X3),
    c_0_2681,
    [final] ).

cnf(c_0_3644,plain,
    ti(fun(fun(X1,X2),fun(fun(X3,X1),fun(X3,X2))),combb(X1,X2,X3)) = combb(X1,X2,X3),
    c_0_2682,
    [final] ).

cnf(c_0_3645,plain,
    ( hBOOL(hAPP(bool,bool,fNot,X1))
    | hBOOL(X1) ),
    c_0_2683,
    [final] ).

cnf(c_0_3646,plain,
    ( hAPP(nat,nat,suc,X1) = hAPP(nat,nat,suc,X2)
    | X1 != X2 ),
    c_0_2684,
    [final] ).

cnf(c_0_3647,plain,
    ti(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1427655034_mktop) = arrow_1427655034_mktop,
    c_0_2685,
    [final] ).

cnf(c_0_3648,plain,
    ti(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1278947948_mkbot) = arrow_1278947948_mkbot,
    c_0_2686,
    [final] ).

cnf(c_0_3649,plain,
    hAPP(nat,nat,suc,X1) != zero_zero(nat),
    c_0_2687,
    [final] ).

cnf(c_0_3650,plain,
    hAPP(nat,nat,suc,X1) != zero_zero(nat),
    c_0_2688,
    [final] ).

cnf(c_0_3651,plain,
    hAPP(nat,nat,suc,X1) != zero_zero(nat),
    c_0_2689,
    [final] ).

cnf(c_0_3652,plain,
    hAPP(nat,nat,suc,X1) != zero_zero(nat),
    c_0_2690,
    [final] ).

cnf(c_0_3653,plain,
    hAPP(nat,nat,suc,X1) != zero_zero(nat),
    c_0_2691,
    [final] ).

cnf(c_0_3654,plain,
    hAPP(nat,nat,suc,X1) != zero_zero(nat),
    c_0_2692,
    [final] ).

cnf(c_0_3655,plain,
    ti(fun(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1))),hilbert_inv_into(X1,X2)) = hilbert_inv_into(X1,X2),
    c_0_2693,
    [final] ).

cnf(c_0_3656,plain,
    hAPP(nat,nat,suc,X1) != X1,
    c_0_2694,
    [final] ).

cnf(c_0_3657,plain,
    hAPP(nat,nat,suc,X1) != X1,
    c_0_2695,
    [final] ).

cnf(c_0_3658,plain,
    ti(fun(fun(product_prod(X1,X2),bool),fun(X1,fun(X2,bool))),in_rel(X1,X2)) = in_rel(X1,X2),
    c_0_2696,
    [final] ).

cnf(c_0_3659,plain,
    ti(fun(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool))),image(X1,X2)) = image(X1,X2),
    c_0_2697,
    [final] ).

cnf(c_0_3660,plain,
    hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2) = ti(fun(X1,bool),X2),
    c_0_2698,
    [final] ).

cnf(c_0_3661,plain,
    ti(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),arrow_1111136790e_Prof) = arrow_1111136790e_Prof,
    c_0_2699,
    [final] ).

cnf(c_0_3662,plain,
    hAPP(fun(product_unit,bool),nat,finite_card(product_unit),top_top(fun(product_unit,bool))) = one_one(nat),
    c_0_2700,
    [final] ).

cnf(c_0_3663,plain,
    ( hAPP(X1,X2,top_top(fun(X1,X2)),X3) = top_top(X2)
    | ~ top(X2) ),
    c_0_2701,
    [final] ).

cnf(c_0_3664,plain,
    ti(fun(fun(X1,X2),fun(fun(X1,bool),bool)),inj_on(X1,X2)) = inj_on(X1,X2),
    c_0_2702,
    [final] ).

cnf(c_0_3665,plain,
    hAPP(X1,X1,combi(X1),X2) = ti(X1,X2),
    c_0_2703,
    [final] ).

cnf(c_0_3666,plain,
    ( hAPP(nat,nat,suc,esk96_1(X1)) = X1
    | X1 = zero_zero(nat) ),
    c_0_2704,
    [final] ).

cnf(c_0_3667,plain,
    ( hAPP(nat,nat,suc,esk95_1(X1)) = X1
    | X1 = zero_zero(nat) ),
    c_0_2705,
    [final] ).

cnf(c_0_3668,plain,
    hAPP(nat,nat,suc,zero_zero(nat)) = one_one(nat),
    c_0_2706,
    [final] ).

cnf(c_0_3669,plain,
    ti(fun(X1,fun(X2,product_prod(X1,X2))),product_Pair(X1,X2)) = product_Pair(X1,X2),
    c_0_2707,
    [final] ).

cnf(c_0_3670,plain,
    ti(fun(bool,fun(X1,fun(X1,X1))),if(X1)) = if(X1),
    c_0_2708,
    [final] ).

cnf(c_0_3671,plain,
    ( ti(fun(X1,fun(X1,fun(X1,bool))),ord_atLeastLessThan(X1)) = ord_atLeastLessThan(X1)
    | ~ linorder(X1) ),
    c_0_2709,
    [final] ).

cnf(c_0_3672,plain,
    ti(fun(X1,fun(fun(X1,bool),bool)),member(X1)) = member(X1),
    c_0_2710,
    [final] ).

cnf(c_0_3673,plain,
    ti(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),arrow_2064824852le_Lin) = arrow_2064824852le_Lin,
    c_0_2711,
    [final] ).

cnf(c_0_3674,plain,
    ti(fun(fun(X1,bool),fun(X1,bool)),collect(X1)) = collect(X1),
    c_0_2712,
    [final] ).

cnf(c_0_3675,plain,
    ti(fun(X1,fun(X2,X1)),combk(X1,X2)) = combk(X1,X2),
    c_0_2713,
    [final] ).

cnf(c_0_3676,plain,
    ( ti(fun(X1,fun(X1,X1)),plus_plus(X1)) = plus_plus(X1)
    | ~ cancel_semigroup_add(X1) ),
    c_0_2714,
    [final] ).

cnf(c_0_3677,plain,
    ( ti(fun(X1,fun(X1,X1)),plus_plus(X1)) = plus_plus(X1)
    | ~ ab_semigroup_add(X1) ),
    c_0_2715,
    [final] ).

cnf(c_0_3678,plain,
    ( ti(fun(X1,fun(X1,X1)),plus_plus(X1)) = plus_plus(X1)
    | ~ monoid_add(X1) ),
    c_0_2716,
    [final] ).

cnf(c_0_3679,plain,
    ( ti(fun(X1,fun(X1,bool)),ord_less_eq(X1)) = ord_less_eq(X1)
    | ~ ord(X1) ),
    c_0_2717,
    [final] ).

cnf(c_0_3680,plain,
    ( ti(fun(X1,fun(X1,bool)),ord_less(X1)) = ord_less(X1)
    | ~ ord(X1) ),
    c_0_2718,
    [final] ).

cnf(c_0_3681,plain,
    ti(fun(X1,fun(X1,bool)),fequal(X1)) = fequal(X1),
    c_0_2719,
    [final] ).

cnf(c_0_3682,plain,
    ti(fun(fun(X1,bool),bool),finite_finite_1(X1)) = finite_finite_1(X1),
    c_0_2720,
    [final] ).

cnf(c_0_3683,plain,
    ti(fun(fun(X1,bool),nat),finite_card(X1)) = finite_card(X1),
    c_0_2721,
    [final] ).

cnf(c_0_3684,plain,
    ti(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),lba) = lba,
    c_0_2722,
    [final] ).

cnf(c_0_3685,plain,
    ti(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),lab) = lab,
    c_0_2723,
    [final] ).

cnf(c_0_3686,plain,
    ti(fun(bool,fun(bool,bool)),fdisj) = fdisj,
    c_0_2724,
    [final] ).

cnf(c_0_3687,plain,
    ti(fun(bool,fun(bool,bool)),fconj) = fconj,
    c_0_2725,
    [final] ).

cnf(c_0_3688,plain,
    ( ti(fun(X1,bool),ring_1_Ints(X1)) = ring_1_Ints(X1)
    | ~ ring_1(X1) ),
    c_0_2726,
    [final] ).

cnf(c_0_3689,plain,
    ( ti(X1,X2) = zero_zero(X1)
    | ~ zero(X1)
    | ti(X1,X2) != zero_zero(X1) ),
    c_0_2727,
    [final] ).

cnf(c_0_3690,plain,
    ( ti(X1,X2) = zero_zero(X1)
    | ~ zero(X1)
    | ti(X1,X2) != zero_zero(X1) ),
    c_0_2728,
    [final] ).

cnf(c_0_3691,plain,
    ( ti(X1,X2) = one_one(X1)
    | ~ one(X1)
    | ti(X1,X2) != one_one(X1) ),
    c_0_2729,
    [final] ).

cnf(c_0_3692,plain,
    ( ti(X1,X2) = one_one(X1)
    | ~ one(X1)
    | ti(X1,X2) != one_one(X1) ),
    c_0_2730,
    [final] ).

cnf(c_0_3693,plain,
    ti(X1,ti(X1,X2)) = ti(X1,X2),
    c_0_2731,
    [final] ).

cnf(c_0_3694,plain,
    ti(fun(X1,X1),combi(X1)) = combi(X1),
    c_0_2732,
    [final] ).

cnf(c_0_3695,plain,
    ( finite_finite(product_prod(X1,X2))
    | ~ finite_finite(X1)
    | ~ finite_finite(X2) ),
    c_0_2733,
    [final] ).

cnf(c_0_3696,plain,
    ( finite_finite(sum_sum(X1,X2))
    | ~ finite_finite(X1)
    | ~ finite_finite(X2) ),
    c_0_2734,
    [final] ).

cnf(c_0_3697,plain,
    ( finite_finite(fun(X1,X2))
    | ~ finite_finite(X1)
    | ~ finite_finite(X2) ),
    c_0_2735,
    [final] ).

cnf(c_0_3698,plain,
    ( ord(fun(X1,X2))
    | ~ ord(X2) ),
    c_0_2736,
    [final] ).

cnf(c_0_3699,plain,
    ( top(fun(X1,X2))
    | ~ top(X2) ),
    c_0_2737,
    [final] ).

cnf(c_0_3700,plain,
    ( order(fun(X1,X2))
    | ~ order(X2) ),
    c_0_2738,
    [final] ).

cnf(c_0_3701,plain,
    ( preorder(fun(X1,X2))
    | ~ preorder(X2) ),
    c_0_2739,
    [final] ).

cnf(c_0_3702,plain,
    ti(fun(arrow_660593299e_indi,nat),h) = h,
    c_0_2740,
    [final] ).

cnf(c_0_3703,plain,
    ti(fun(bool,bool),fNot) = fNot,
    c_0_2741,
    [final] ).

cnf(c_0_3704,plain,
    ti(fun(nat,nat),suc) = suc,
    c_0_2742,
    [final] ).

cnf(c_0_3705,plain,
    ( ti(X1,top_top(X1)) = top_top(X1)
    | ~ top(X1) ),
    c_0_2743,
    [final] ).

cnf(c_0_3706,plain,
    ( ti(X1,zero_zero(X1)) = zero_zero(X1)
    | ~ zero(X1) ),
    c_0_2744,
    [final] ).

cnf(c_0_3707,plain,
    ( ti(X1,one_one(X1)) = one_one(X1)
    | ~ one(X1) ),
    c_0_2745,
    [final] ).

cnf(c_0_3708,plain,
    ( ti(bool,X1) = fFalse
    | ti(bool,X1) = fTrue ),
    c_0_2746,
    [final] ).

cnf(c_0_3709,plain,
    ( ti(bool,X1) = fFalse
    | ti(bool,X1) = fTrue ),
    c_0_2747,
    [final] ).

cnf(c_0_3710,plain,
    ti(X1,undefined(X1)) = undefined(X1),
    c_0_2748,
    [final] ).

cnf(c_0_3711,plain,
    ( zero_zero(X1) != one_one(X1)
    | ~ zero_neq_one(X1) ),
    c_0_2749,
    [final] ).

cnf(c_0_3712,plain,
    ( zero_zero(X1) != one_one(X1)
    | ~ zero_neq_one(X1) ),
    c_0_2750,
    [final] ).

cnf(c_0_3713,plain,
    ( finite_finite(option(X1))
    | ~ finite_finite(X1) ),
    c_0_2751,
    [final] ).

cnf(c_0_3714,plain,
    ti(nat,n) = n,
    c_0_2752,
    [final] ).

cnf(c_0_3715,plain,
    ti(arrow_490897120le_alt,e) = e,
    c_0_2753,
    [final] ).

cnf(c_0_3716,plain,
    ti(arrow_490897120le_alt,b) = b,
    c_0_2754,
    [final] ).

cnf(c_0_3717,plain,
    ti(arrow_490897120le_alt,a) = a,
    c_0_2755,
    [final] ).

cnf(c_0_3718,plain,
    ti(bool,fTrue) = fTrue,
    c_0_2756,
    [final] ).

cnf(c_0_3719,plain,
    ti(bool,fFalse) = fFalse,
    c_0_2757,
    [final] ).

cnf(c_0_3720,plain,
    hBOOL(fTrue),
    c_0_2758,
    [final] ).

cnf(c_0_3721,plain,
    finite_finite(product_unit),
    c_0_2759,
    [final] ).

cnf(c_0_3722,plain,
    ord(bool),
    c_0_2760,
    [final] ).

cnf(c_0_3723,plain,
    top(bool),
    c_0_2761,
    [final] ).

cnf(c_0_3724,plain,
    order(bool),
    c_0_2762,
    [final] ).

cnf(c_0_3725,plain,
    finite_finite(bool),
    c_0_2763,
    [final] ).

cnf(c_0_3726,plain,
    preorder(bool),
    c_0_2764,
    [final] ).

cnf(c_0_3727,plain,
    one(nat),
    c_0_2765,
    [final] ).

cnf(c_0_3728,plain,
    zero(nat),
    c_0_2766,
    [final] ).

cnf(c_0_3729,plain,
    ord(nat),
    c_0_2767,
    [final] ).

cnf(c_0_3730,plain,
    order(nat),
    c_0_2768,
    [final] ).

cnf(c_0_3731,plain,
    monoid_add(nat),
    c_0_2769,
    [final] ).

cnf(c_0_3732,plain,
    linorder(nat),
    c_0_2770,
    [final] ).

cnf(c_0_3733,plain,
    preorder(nat),
    c_0_2771,
    [final] ).

cnf(c_0_3734,plain,
    zero_neq_one(nat),
    c_0_2772,
    [final] ).

cnf(c_0_3735,plain,
    comm_semiring_1(nat),
    c_0_2773,
    [final] ).

cnf(c_0_3736,plain,
    comm_monoid_add(nat),
    c_0_2774,
    [final] ).

cnf(c_0_3737,plain,
    ab_semigroup_add(nat),
    c_0_2775,
    [final] ).

cnf(c_0_3738,plain,
    linordered_semidom(nat),
    c_0_2776,
    [final] ).

cnf(c_0_3739,plain,
    cancel_semigroup_add(nat),
    c_0_2777,
    [final] ).

cnf(c_0_3740,plain,
    cancel146912293up_add(nat),
    c_0_2778,
    [final] ).

cnf(c_0_3741,plain,
    ordere216010020id_add(nat),
    c_0_2779,
    [final] ).

cnf(c_0_3742,plain,
    ordere779506340up_add(nat),
    c_0_2780,
    [final] ).

cnf(c_0_3743,plain,
    ordere236663937imp_le(nat),
    c_0_2781,
    [final] ).

cnf(c_0_3744,plain,
    ordere223160158up_add(nat),
    c_0_2782,
    [final] ).

cnf(c_0_3745,plain,
    semiri456707255roduct(nat),
    c_0_2783,
    [final] ).

cnf(c_0_3746,plain,
    b != a,
    c_0_2784,
    [final] ).

cnf(c_0_3747,plain,
    d != c,
    c_0_2785,
    [final] ).

% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
cnf(c_0_2786_0,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))),lab)),lba))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))))) ),
    inference(literals_permutation,[status(thm)],[c_0_2786]) ).

cnf(c_0_2786_1,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e))))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))),lab)),lba)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2786]) ).

cnf(c_0_2787_0,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),lab)),lba))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))))) ),
    inference(literals_permutation,[status(thm)],[c_0_2787]) ).

cnf(c_0_2787_1,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e))))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),lab)),lba)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2787]) ).

cnf(c_0_2788_0,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,p)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))))) ),
    inference(literals_permutation,[status(thm)],[c_0_2788]) ).

cnf(c_0_2788_1,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e))))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,p))) ),
    inference(literals_permutation,[status(thm)],[c_0_2788]) ).

cnf(c_0_2789_0,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e))))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))),lab)),lba)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2789]) ).

cnf(c_0_2789_1,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))),lab)),lba))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))))) ),
    inference(literals_permutation,[status(thm)],[c_0_2789]) ).

cnf(c_0_2790_0,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e))))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),lab)),lba)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2790]) ).

cnf(c_0_2790_1,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),lab)),lba))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))))) ),
    inference(literals_permutation,[status(thm)],[c_0_2790]) ).

cnf(c_0_2791_0,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e))))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,p))) ),
    inference(literals_permutation,[status(thm)],[c_0_2791]) ).

cnf(c_0_2791_1,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,p)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))))) ),
    inference(literals_permutation,[status(thm)],[c_0_2791]) ).

cnf(c_0_2799_0,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),X1))),lab)),lba))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),sk1_esk28_0)) ),
    inference(literals_permutation,[status(thm)],[c_0_2799]) ).

cnf(c_0_2799_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),sk1_esk28_0))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),X1))),lab)),lba)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2799]) ).

cnf(c_0_2800_0,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),X1))),lab)),lba))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),sk1_esk27_0)) ),
    inference(literals_permutation,[status(thm)],[c_0_2800]) ).

cnf(c_0_2800_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),sk1_esk27_0))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),X1))),lab)),lba)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2800]) ).

cnf(c_0_2801_0,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),X1))),lab)),lba))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2801]) ).

cnf(c_0_2801_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),X1))),lab)),lba)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2801]) ).

cnf(c_0_2803_0,axiom,
    ( hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(fun(product_prod(X1,X2),bool),fun(fun(product_prod(X1,X2),bool),bool),ord_less_eq(fun(product_prod(X1,X2),bool)),X3),X4))
    | ~ hBOOL(hAPP(fun(X1,fun(X2,bool)),bool,hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,fun(X2,bool)),bool),ord_less_eq(fun(X1,fun(X2,bool))),hAPP(fun(product_prod(X1,X2),bool),fun(X1,fun(X2,bool)),hAPP(fun(X1,fun(fun(product_prod(X1,X2),bool),fun(X2,bool))),fun(fun(product_prod(X1,X2),bool),fun(X1,fun(X2,bool))),combc(X1,fun(product_prod(X1,X2),bool),fun(X2,bool)),hAPP(fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),fun(X1,fun(fun(product_prod(X1,X2),bool),fun(X2,bool))),hAPP(fun(fun(X2,fun(fun(product_prod(X1,X2),bool),bool)),fun(fun(product_prod(X1,X2),bool),fun(X2,bool))),fun(fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),fun(X1,fun(fun(product_prod(X1,X2),bool),fun(X2,bool)))),combb(fun(X2,fun(fun(product_prod(X1,X2),bool),bool)),fun(fun(product_prod(X1,X2),bool),fun(X2,bool)),X1),combc(X2,fun(product_prod(X1,X2),bool),bool)),hAPP(fun(X1,fun(X2,product_prod(X1,X2))),fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),hAPP(fun(fun(X2,product_prod(X1,X2)),fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),fun(fun(X1,fun(X2,product_prod(X1,X2))),fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool)))),combb(fun(X2,product_prod(X1,X2)),fun(X2,fun(fun(product_prod(X1,X2),bool),bool)),X1),hAPP(fun(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool)),fun(fun(X2,product_prod(X1,X2)),fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),combb(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),X2),member(product_prod(X1,X2)))),product_Pair(X1,X2)))),X3)),hAPP(fun(product_prod(X1,X2),bool),fun(X1,fun(X2,bool)),hAPP(fun(X1,fun(fun(product_prod(X1,X2),bool),fun(X2,bool))),fun(fun(product_prod(X1,X2),bool),fun(X1,fun(X2,bool))),combc(X1,fun(product_prod(X1,X2),bool),fun(X2,bool)),hAPP(fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),fun(X1,fun(fun(product_prod(X1,X2),bool),fun(X2,bool))),hAPP(fun(fun(X2,fun(fun(product_prod(X1,X2),bool),bool)),fun(fun(product_prod(X1,X2),bool),fun(X2,bool))),fun(fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),fun(X1,fun(fun(product_prod(X1,X2),bool),fun(X2,bool)))),combb(fun(X2,fun(fun(product_prod(X1,X2),bool),bool)),fun(fun(product_prod(X1,X2),bool),fun(X2,bool)),X1),combc(X2,fun(product_prod(X1,X2),bool),bool)),hAPP(fun(X1,fun(X2,product_prod(X1,X2))),fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),hAPP(fun(fun(X2,product_prod(X1,X2)),fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),fun(fun(X1,fun(X2,product_prod(X1,X2))),fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool)))),combb(fun(X2,product_prod(X1,X2)),fun(X2,fun(fun(product_prod(X1,X2),bool),bool)),X1),hAPP(fun(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool)),fun(fun(X2,product_prod(X1,X2)),fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),combb(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),X2),member(product_prod(X1,X2)))),product_Pair(X1,X2)))),X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_2803]) ).

cnf(c_0_2803_1,axiom,
    ( ~ hBOOL(hAPP(fun(X1,fun(X2,bool)),bool,hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,fun(X2,bool)),bool),ord_less_eq(fun(X1,fun(X2,bool))),hAPP(fun(product_prod(X1,X2),bool),fun(X1,fun(X2,bool)),hAPP(fun(X1,fun(fun(product_prod(X1,X2),bool),fun(X2,bool))),fun(fun(product_prod(X1,X2),bool),fun(X1,fun(X2,bool))),combc(X1,fun(product_prod(X1,X2),bool),fun(X2,bool)),hAPP(fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),fun(X1,fun(fun(product_prod(X1,X2),bool),fun(X2,bool))),hAPP(fun(fun(X2,fun(fun(product_prod(X1,X2),bool),bool)),fun(fun(product_prod(X1,X2),bool),fun(X2,bool))),fun(fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),fun(X1,fun(fun(product_prod(X1,X2),bool),fun(X2,bool)))),combb(fun(X2,fun(fun(product_prod(X1,X2),bool),bool)),fun(fun(product_prod(X1,X2),bool),fun(X2,bool)),X1),combc(X2,fun(product_prod(X1,X2),bool),bool)),hAPP(fun(X1,fun(X2,product_prod(X1,X2))),fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),hAPP(fun(fun(X2,product_prod(X1,X2)),fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),fun(fun(X1,fun(X2,product_prod(X1,X2))),fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool)))),combb(fun(X2,product_prod(X1,X2)),fun(X2,fun(fun(product_prod(X1,X2),bool),bool)),X1),hAPP(fun(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool)),fun(fun(X2,product_prod(X1,X2)),fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),combb(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),X2),member(product_prod(X1,X2)))),product_Pair(X1,X2)))),X3)),hAPP(fun(product_prod(X1,X2),bool),fun(X1,fun(X2,bool)),hAPP(fun(X1,fun(fun(product_prod(X1,X2),bool),fun(X2,bool))),fun(fun(product_prod(X1,X2),bool),fun(X1,fun(X2,bool))),combc(X1,fun(product_prod(X1,X2),bool),fun(X2,bool)),hAPP(fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),fun(X1,fun(fun(product_prod(X1,X2),bool),fun(X2,bool))),hAPP(fun(fun(X2,fun(fun(product_prod(X1,X2),bool),bool)),fun(fun(product_prod(X1,X2),bool),fun(X2,bool))),fun(fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),fun(X1,fun(fun(product_prod(X1,X2),bool),fun(X2,bool)))),combb(fun(X2,fun(fun(product_prod(X1,X2),bool),bool)),fun(fun(product_prod(X1,X2),bool),fun(X2,bool)),X1),combc(X2,fun(product_prod(X1,X2),bool),bool)),hAPP(fun(X1,fun(X2,product_prod(X1,X2))),fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),hAPP(fun(fun(X2,product_prod(X1,X2)),fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),fun(fun(X1,fun(X2,product_prod(X1,X2))),fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool)))),combb(fun(X2,product_prod(X1,X2)),fun(X2,fun(fun(product_prod(X1,X2),bool),bool)),X1),hAPP(fun(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool)),fun(fun(X2,product_prod(X1,X2)),fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),combb(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),X2),member(product_prod(X1,X2)))),product_Pair(X1,X2)))),X4)))
    | hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(fun(product_prod(X1,X2),bool),fun(fun(product_prod(X1,X2),bool),bool),ord_less_eq(fun(product_prod(X1,X2),bool)),X3),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_2803]) ).

cnf(c_0_2804_0,axiom,
    ( hBOOL(hAPP(fun(X1,fun(X2,bool)),bool,hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,fun(X2,bool)),bool),ord_less_eq(fun(X1,fun(X2,bool))),hAPP(fun(product_prod(X1,X2),bool),fun(X1,fun(X2,bool)),hAPP(fun(X1,fun(fun(product_prod(X1,X2),bool),fun(X2,bool))),fun(fun(product_prod(X1,X2),bool),fun(X1,fun(X2,bool))),combc(X1,fun(product_prod(X1,X2),bool),fun(X2,bool)),hAPP(fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),fun(X1,fun(fun(product_prod(X1,X2),bool),fun(X2,bool))),hAPP(fun(fun(X2,fun(fun(product_prod(X1,X2),bool),bool)),fun(fun(product_prod(X1,X2),bool),fun(X2,bool))),fun(fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),fun(X1,fun(fun(product_prod(X1,X2),bool),fun(X2,bool)))),combb(fun(X2,fun(fun(product_prod(X1,X2),bool),bool)),fun(fun(product_prod(X1,X2),bool),fun(X2,bool)),X1),combc(X2,fun(product_prod(X1,X2),bool),bool)),hAPP(fun(X1,fun(X2,product_prod(X1,X2))),fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),hAPP(fun(fun(X2,product_prod(X1,X2)),fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),fun(fun(X1,fun(X2,product_prod(X1,X2))),fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool)))),combb(fun(X2,product_prod(X1,X2)),fun(X2,fun(fun(product_prod(X1,X2),bool),bool)),X1),hAPP(fun(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool)),fun(fun(X2,product_prod(X1,X2)),fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),combb(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),X2),member(product_prod(X1,X2)))),product_Pair(X1,X2)))),X3)),hAPP(fun(product_prod(X1,X2),bool),fun(X1,fun(X2,bool)),hAPP(fun(X1,fun(fun(product_prod(X1,X2),bool),fun(X2,bool))),fun(fun(product_prod(X1,X2),bool),fun(X1,fun(X2,bool))),combc(X1,fun(product_prod(X1,X2),bool),fun(X2,bool)),hAPP(fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),fun(X1,fun(fun(product_prod(X1,X2),bool),fun(X2,bool))),hAPP(fun(fun(X2,fun(fun(product_prod(X1,X2),bool),bool)),fun(fun(product_prod(X1,X2),bool),fun(X2,bool))),fun(fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),fun(X1,fun(fun(product_prod(X1,X2),bool),fun(X2,bool)))),combb(fun(X2,fun(fun(product_prod(X1,X2),bool),bool)),fun(fun(product_prod(X1,X2),bool),fun(X2,bool)),X1),combc(X2,fun(product_prod(X1,X2),bool),bool)),hAPP(fun(X1,fun(X2,product_prod(X1,X2))),fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),hAPP(fun(fun(X2,product_prod(X1,X2)),fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),fun(fun(X1,fun(X2,product_prod(X1,X2))),fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool)))),combb(fun(X2,product_prod(X1,X2)),fun(X2,fun(fun(product_prod(X1,X2),bool),bool)),X1),hAPP(fun(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool)),fun(fun(X2,product_prod(X1,X2)),fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),combb(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),X2),member(product_prod(X1,X2)))),product_Pair(X1,X2)))),X4)))
    | ~ hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(fun(product_prod(X1,X2),bool),fun(fun(product_prod(X1,X2),bool),bool),ord_less_eq(fun(product_prod(X1,X2),bool)),X3),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_2804]) ).

cnf(c_0_2804_1,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(fun(product_prod(X1,X2),bool),fun(fun(product_prod(X1,X2),bool),bool),ord_less_eq(fun(product_prod(X1,X2),bool)),X3),X4))
    | hBOOL(hAPP(fun(X1,fun(X2,bool)),bool,hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,fun(X2,bool)),bool),ord_less_eq(fun(X1,fun(X2,bool))),hAPP(fun(product_prod(X1,X2),bool),fun(X1,fun(X2,bool)),hAPP(fun(X1,fun(fun(product_prod(X1,X2),bool),fun(X2,bool))),fun(fun(product_prod(X1,X2),bool),fun(X1,fun(X2,bool))),combc(X1,fun(product_prod(X1,X2),bool),fun(X2,bool)),hAPP(fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),fun(X1,fun(fun(product_prod(X1,X2),bool),fun(X2,bool))),hAPP(fun(fun(X2,fun(fun(product_prod(X1,X2),bool),bool)),fun(fun(product_prod(X1,X2),bool),fun(X2,bool))),fun(fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),fun(X1,fun(fun(product_prod(X1,X2),bool),fun(X2,bool)))),combb(fun(X2,fun(fun(product_prod(X1,X2),bool),bool)),fun(fun(product_prod(X1,X2),bool),fun(X2,bool)),X1),combc(X2,fun(product_prod(X1,X2),bool),bool)),hAPP(fun(X1,fun(X2,product_prod(X1,X2))),fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),hAPP(fun(fun(X2,product_prod(X1,X2)),fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),fun(fun(X1,fun(X2,product_prod(X1,X2))),fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool)))),combb(fun(X2,product_prod(X1,X2)),fun(X2,fun(fun(product_prod(X1,X2),bool),bool)),X1),hAPP(fun(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool)),fun(fun(X2,product_prod(X1,X2)),fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),combb(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),X2),member(product_prod(X1,X2)))),product_Pair(X1,X2)))),X3)),hAPP(fun(product_prod(X1,X2),bool),fun(X1,fun(X2,bool)),hAPP(fun(X1,fun(fun(product_prod(X1,X2),bool),fun(X2,bool))),fun(fun(product_prod(X1,X2),bool),fun(X1,fun(X2,bool))),combc(X1,fun(product_prod(X1,X2),bool),fun(X2,bool)),hAPP(fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),fun(X1,fun(fun(product_prod(X1,X2),bool),fun(X2,bool))),hAPP(fun(fun(X2,fun(fun(product_prod(X1,X2),bool),bool)),fun(fun(product_prod(X1,X2),bool),fun(X2,bool))),fun(fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),fun(X1,fun(fun(product_prod(X1,X2),bool),fun(X2,bool)))),combb(fun(X2,fun(fun(product_prod(X1,X2),bool),bool)),fun(fun(product_prod(X1,X2),bool),fun(X2,bool)),X1),combc(X2,fun(product_prod(X1,X2),bool),bool)),hAPP(fun(X1,fun(X2,product_prod(X1,X2))),fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),hAPP(fun(fun(X2,product_prod(X1,X2)),fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),fun(fun(X1,fun(X2,product_prod(X1,X2))),fun(X1,fun(X2,fun(fun(product_prod(X1,X2),bool),bool)))),combb(fun(X2,product_prod(X1,X2)),fun(X2,fun(fun(product_prod(X1,X2),bool),bool)),X1),hAPP(fun(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool)),fun(fun(X2,product_prod(X1,X2)),fun(X2,fun(fun(product_prod(X1,X2),bool),bool))),combb(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),X2),member(product_prod(X1,X2)))),product_Pair(X1,X2)))),X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_2804]) ).

cnf(c_0_2805_0,axiom,
    ( hAPP(nat,nat,suc,hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),hAPP(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool)),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool))),combb(nat,fun(fun(nat,bool),bool),nat),member(nat)),suc)),X1))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X2))))) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),X1))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,X2)))))
    | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_2805]) ).

cnf(c_0_2805_1,axiom,
    ( ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),X1))
    | hAPP(nat,nat,suc,hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),hAPP(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool)),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool))),combb(nat,fun(fun(nat,bool),bool),nat),member(nat)),suc)),X1))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X2))))) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),X1))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,X2))))) ),
    inference(literals_permutation,[status(thm)],[c_0_2805]) ).

cnf(c_0_2806_0,axiom,
    ( hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),hAPP(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool)),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool))),combb(nat,fun(fun(nat,bool),bool),nat),member(nat)),suc)),X1))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X2)))) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),X1))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,X2)))))
    | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_2806]) ).

cnf(c_0_2806_1,axiom,
    ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),X1))
    | hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),hAPP(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool)),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool))),combb(nat,fun(fun(nat,bool),bool),nat),member(nat)),suc)),X1))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X2)))) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),X1))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,X2))))) ),
    inference(literals_permutation,[status(thm)],[c_0_2806]) ).

cnf(c_0_2807_0,axiom,
    ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6))
    | ~ order(X1)
    | ~ order(X2)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X5,X4)),X6))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,sk1_esk58_6(X1,X2,X5,X6,X3,X4))),hAPP(X1,X2,X5,sk1_esk59_6(X1,X2,X5,X6,X3,X4)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2807]) ).

cnf(c_0_2807_1,axiom,
    ( ~ order(X1)
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6))
    | ~ order(X2)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X5,X4)),X6))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,sk1_esk58_6(X1,X2,X5,X6,X3,X4))),hAPP(X1,X2,X5,sk1_esk59_6(X1,X2,X5,X6,X3,X4)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2807]) ).

cnf(c_0_2807_2,axiom,
    ( ~ order(X2)
    | ~ order(X1)
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X5,X4)),X6))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,sk1_esk58_6(X1,X2,X5,X6,X3,X4))),hAPP(X1,X2,X5,sk1_esk59_6(X1,X2,X5,X6,X3,X4)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2807]) ).

cnf(c_0_2807_3,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
    | ~ order(X2)
    | ~ order(X1)
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X5,X4)),X6))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,sk1_esk58_6(X1,X2,X5,X6,X3,X4))),hAPP(X1,X2,X5,sk1_esk59_6(X1,X2,X5,X6,X3,X4)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2807]) ).

cnf(c_0_2807_4,axiom,
    ( ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X5,X4)),X6))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
    | ~ order(X2)
    | ~ order(X1)
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,sk1_esk58_6(X1,X2,X5,X6,X3,X4))),hAPP(X1,X2,X5,sk1_esk59_6(X1,X2,X5,X6,X3,X4)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2807]) ).

cnf(c_0_2807_5,axiom,
    ( ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,sk1_esk58_6(X1,X2,X5,X6,X3,X4))),hAPP(X1,X2,X5,sk1_esk59_6(X1,X2,X5,X6,X3,X4))))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X5,X4)),X6))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
    | ~ order(X2)
    | ~ order(X1)
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_2807]) ).

cnf(c_0_2808_0,axiom,
    ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6))
    | ~ order(X1)
    | ~ order(X2)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X4)),X6))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X5,sk1_esk48_6(X1,X2,X5,X6,X3,X4))),hAPP(X1,X2,X5,sk1_esk49_6(X1,X2,X5,X6,X3,X4)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2808]) ).

cnf(c_0_2808_1,axiom,
    ( ~ order(X1)
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6))
    | ~ order(X2)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X4)),X6))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X5,sk1_esk48_6(X1,X2,X5,X6,X3,X4))),hAPP(X1,X2,X5,sk1_esk49_6(X1,X2,X5,X6,X3,X4)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2808]) ).

cnf(c_0_2808_2,axiom,
    ( ~ order(X2)
    | ~ order(X1)
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X4)),X6))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X5,sk1_esk48_6(X1,X2,X5,X6,X3,X4))),hAPP(X1,X2,X5,sk1_esk49_6(X1,X2,X5,X6,X3,X4)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2808]) ).

cnf(c_0_2808_3,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
    | ~ order(X2)
    | ~ order(X1)
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X4)),X6))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X5,sk1_esk48_6(X1,X2,X5,X6,X3,X4))),hAPP(X1,X2,X5,sk1_esk49_6(X1,X2,X5,X6,X3,X4)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2808]) ).

cnf(c_0_2808_4,axiom,
    ( ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X4)),X6))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
    | ~ order(X2)
    | ~ order(X1)
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X5,sk1_esk48_6(X1,X2,X5,X6,X3,X4))),hAPP(X1,X2,X5,sk1_esk49_6(X1,X2,X5,X6,X3,X4)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2808]) ).

cnf(c_0_2808_5,axiom,
    ( ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X5,sk1_esk48_6(X1,X2,X5,X6,X3,X4))),hAPP(X1,X2,X5,sk1_esk49_6(X1,X2,X5,X6,X3,X4))))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X4)),X6))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
    | ~ order(X2)
    | ~ order(X1)
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_2808]) ).

cnf(c_0_2809_0,axiom,
    ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5))
    | ~ order(X1)
    | ~ order(X2)
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X4)),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X4))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,sk1_esk43_6(X1,X2,X6,X3,X4,X5))),hAPP(X1,X2,X3,sk1_esk42_6(X1,X2,X6,X3,X4,X5)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2809]) ).

cnf(c_0_2809_1,axiom,
    ( ~ order(X1)
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5))
    | ~ order(X2)
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X4)),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X4))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,sk1_esk43_6(X1,X2,X6,X3,X4,X5))),hAPP(X1,X2,X3,sk1_esk42_6(X1,X2,X6,X3,X4,X5)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2809]) ).

cnf(c_0_2809_2,axiom,
    ( ~ order(X2)
    | ~ order(X1)
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X4)),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X4))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,sk1_esk43_6(X1,X2,X6,X3,X4,X5))),hAPP(X1,X2,X3,sk1_esk42_6(X1,X2,X6,X3,X4,X5)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2809]) ).

cnf(c_0_2809_3,axiom,
    ( ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X4)),X5))
    | ~ order(X2)
    | ~ order(X1)
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X4))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,sk1_esk43_6(X1,X2,X6,X3,X4,X5))),hAPP(X1,X2,X3,sk1_esk42_6(X1,X2,X6,X3,X4,X5)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2809]) ).

cnf(c_0_2809_4,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X4))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X4)),X5))
    | ~ order(X2)
    | ~ order(X1)
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,sk1_esk43_6(X1,X2,X6,X3,X4,X5))),hAPP(X1,X2,X3,sk1_esk42_6(X1,X2,X6,X3,X4,X5)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2809]) ).

cnf(c_0_2809_5,axiom,
    ( ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,sk1_esk43_6(X1,X2,X6,X3,X4,X5))),hAPP(X1,X2,X3,sk1_esk42_6(X1,X2,X6,X3,X4,X5))))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X4))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X4)),X5))
    | ~ order(X2)
    | ~ order(X1)
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_2809]) ).

cnf(c_0_2810_0,axiom,
    ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5))
    | ~ ord(X1)
    | ~ order(X2)
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,X4)),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X4))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,sk1_esk41_6(X1,X2,X6,X3,X4,X5))),hAPP(X1,X2,X3,sk1_esk40_6(X1,X2,X6,X3,X4,X5)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2810]) ).

cnf(c_0_2810_1,axiom,
    ( ~ ord(X1)
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5))
    | ~ order(X2)
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,X4)),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X4))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,sk1_esk41_6(X1,X2,X6,X3,X4,X5))),hAPP(X1,X2,X3,sk1_esk40_6(X1,X2,X6,X3,X4,X5)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2810]) ).

cnf(c_0_2810_2,axiom,
    ( ~ order(X2)
    | ~ ord(X1)
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,X4)),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X4))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,sk1_esk41_6(X1,X2,X6,X3,X4,X5))),hAPP(X1,X2,X3,sk1_esk40_6(X1,X2,X6,X3,X4,X5)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2810]) ).

cnf(c_0_2810_3,axiom,
    ( ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,X4)),X5))
    | ~ order(X2)
    | ~ ord(X1)
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X4))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,sk1_esk41_6(X1,X2,X6,X3,X4,X5))),hAPP(X1,X2,X3,sk1_esk40_6(X1,X2,X6,X3,X4,X5)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2810]) ).

cnf(c_0_2810_4,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X4))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,X4)),X5))
    | ~ order(X2)
    | ~ ord(X1)
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,sk1_esk41_6(X1,X2,X6,X3,X4,X5))),hAPP(X1,X2,X3,sk1_esk40_6(X1,X2,X6,X3,X4,X5)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2810]) ).

cnf(c_0_2810_5,axiom,
    ( ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,sk1_esk41_6(X1,X2,X6,X3,X4,X5))),hAPP(X1,X2,X3,sk1_esk40_6(X1,X2,X6,X3,X4,X5))))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X4))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,X4)),X5))
    | ~ order(X2)
    | ~ ord(X1)
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_2810]) ).

cnf(c_0_2811_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4)))
    | ~ order(X1)
    | ~ order(X2)
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X3),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X3)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X6,sk1_esk57_6(X1,X2,X5,X6,X3,X4))),hAPP(X2,X1,X6,sk1_esk56_6(X1,X2,X5,X6,X3,X4)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2811]) ).

cnf(c_0_2811_1,axiom,
    ( ~ order(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4)))
    | ~ order(X2)
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X3),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X3)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X6,sk1_esk57_6(X1,X2,X5,X6,X3,X4))),hAPP(X2,X1,X6,sk1_esk56_6(X1,X2,X5,X6,X3,X4)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2811]) ).

cnf(c_0_2811_2,axiom,
    ( ~ order(X2)
    | ~ order(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4)))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X3),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X3)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X6,sk1_esk57_6(X1,X2,X5,X6,X3,X4))),hAPP(X2,X1,X6,sk1_esk56_6(X1,X2,X5,X6,X3,X4)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2811]) ).

cnf(c_0_2811_3,axiom,
    ( ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X3),X4))
    | ~ order(X2)
    | ~ order(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X3)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X6,sk1_esk57_6(X1,X2,X5,X6,X3,X4))),hAPP(X2,X1,X6,sk1_esk56_6(X1,X2,X5,X6,X3,X4)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2811]) ).

cnf(c_0_2811_4,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X3)))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X3),X4))
    | ~ order(X2)
    | ~ order(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X6,sk1_esk57_6(X1,X2,X5,X6,X3,X4))),hAPP(X2,X1,X6,sk1_esk56_6(X1,X2,X5,X6,X3,X4)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2811]) ).

cnf(c_0_2811_5,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X6,sk1_esk57_6(X1,X2,X5,X6,X3,X4))),hAPP(X2,X1,X6,sk1_esk56_6(X1,X2,X5,X6,X3,X4))))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X3)))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X3),X4))
    | ~ order(X2)
    | ~ order(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_2811]) ).

cnf(c_0_2812_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4)))
    | ~ order(X1)
    | ~ order(X2)
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X3),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),hAPP(X2,X1,X6,X3)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X6,sk1_esk55_6(X1,X2,X5,X6,X3,X4))),hAPP(X2,X1,X6,sk1_esk54_6(X1,X2,X5,X6,X3,X4)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2812]) ).

cnf(c_0_2812_1,axiom,
    ( ~ order(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4)))
    | ~ order(X2)
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X3),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),hAPP(X2,X1,X6,X3)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X6,sk1_esk55_6(X1,X2,X5,X6,X3,X4))),hAPP(X2,X1,X6,sk1_esk54_6(X1,X2,X5,X6,X3,X4)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2812]) ).

cnf(c_0_2812_2,axiom,
    ( ~ order(X2)
    | ~ order(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4)))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X3),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),hAPP(X2,X1,X6,X3)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X6,sk1_esk55_6(X1,X2,X5,X6,X3,X4))),hAPP(X2,X1,X6,sk1_esk54_6(X1,X2,X5,X6,X3,X4)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2812]) ).

cnf(c_0_2812_3,axiom,
    ( ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X3),X4))
    | ~ order(X2)
    | ~ order(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),hAPP(X2,X1,X6,X3)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X6,sk1_esk55_6(X1,X2,X5,X6,X3,X4))),hAPP(X2,X1,X6,sk1_esk54_6(X1,X2,X5,X6,X3,X4)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2812]) ).

cnf(c_0_2812_4,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),hAPP(X2,X1,X6,X3)))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X3),X4))
    | ~ order(X2)
    | ~ order(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X6,sk1_esk55_6(X1,X2,X5,X6,X3,X4))),hAPP(X2,X1,X6,sk1_esk54_6(X1,X2,X5,X6,X3,X4)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2812]) ).

cnf(c_0_2812_5,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X6,sk1_esk55_6(X1,X2,X5,X6,X3,X4))),hAPP(X2,X1,X6,sk1_esk54_6(X1,X2,X5,X6,X3,X4))))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),hAPP(X2,X1,X6,X3)))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X3),X4))
    | ~ order(X2)
    | ~ order(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_2812]) ).

cnf(c_0_2813_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6)))
    | ~ order(X1)
    | ~ order(X2)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X5)))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X5),X6))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X4,sk1_esk46_6(X1,X2,X6,X3,X4,X5))),hAPP(X2,X1,X4,sk1_esk47_6(X1,X2,X6,X3,X4,X5)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2813]) ).

cnf(c_0_2813_1,axiom,
    ( ~ order(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6)))
    | ~ order(X2)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X5)))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X5),X6))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X4,sk1_esk46_6(X1,X2,X6,X3,X4,X5))),hAPP(X2,X1,X4,sk1_esk47_6(X1,X2,X6,X3,X4,X5)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2813]) ).

cnf(c_0_2813_2,axiom,
    ( ~ order(X2)
    | ~ order(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X5)))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X5),X6))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X4,sk1_esk46_6(X1,X2,X6,X3,X4,X5))),hAPP(X2,X1,X4,sk1_esk47_6(X1,X2,X6,X3,X4,X5)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2813]) ).

cnf(c_0_2813_3,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X5)))
    | ~ order(X2)
    | ~ order(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6)))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X5),X6))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X4,sk1_esk46_6(X1,X2,X6,X3,X4,X5))),hAPP(X2,X1,X4,sk1_esk47_6(X1,X2,X6,X3,X4,X5)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2813]) ).

cnf(c_0_2813_4,axiom,
    ( ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X5),X6))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X5)))
    | ~ order(X2)
    | ~ order(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X4,sk1_esk46_6(X1,X2,X6,X3,X4,X5))),hAPP(X2,X1,X4,sk1_esk47_6(X1,X2,X6,X3,X4,X5)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2813]) ).

cnf(c_0_2813_5,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X4,sk1_esk46_6(X1,X2,X6,X3,X4,X5))),hAPP(X2,X1,X4,sk1_esk47_6(X1,X2,X6,X3,X4,X5))))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X5),X6))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X5)))
    | ~ order(X2)
    | ~ order(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6))) ),
    inference(literals_permutation,[status(thm)],[c_0_2813]) ).

cnf(c_0_2814_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6)))
    | ~ order(X1)
    | ~ order(X2)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),hAPP(X2,X1,X4,X5)))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X5),X6))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X4,sk1_esk44_6(X1,X2,X6,X3,X4,X5))),hAPP(X2,X1,X4,sk1_esk45_6(X1,X2,X6,X3,X4,X5)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2814]) ).

cnf(c_0_2814_1,axiom,
    ( ~ order(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6)))
    | ~ order(X2)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),hAPP(X2,X1,X4,X5)))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X5),X6))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X4,sk1_esk44_6(X1,X2,X6,X3,X4,X5))),hAPP(X2,X1,X4,sk1_esk45_6(X1,X2,X6,X3,X4,X5)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2814]) ).

cnf(c_0_2814_2,axiom,
    ( ~ order(X2)
    | ~ order(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),hAPP(X2,X1,X4,X5)))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X5),X6))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X4,sk1_esk44_6(X1,X2,X6,X3,X4,X5))),hAPP(X2,X1,X4,sk1_esk45_6(X1,X2,X6,X3,X4,X5)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2814]) ).

cnf(c_0_2814_3,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),hAPP(X2,X1,X4,X5)))
    | ~ order(X2)
    | ~ order(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6)))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X5),X6))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X4,sk1_esk44_6(X1,X2,X6,X3,X4,X5))),hAPP(X2,X1,X4,sk1_esk45_6(X1,X2,X6,X3,X4,X5)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2814]) ).

cnf(c_0_2814_4,axiom,
    ( ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X5),X6))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),hAPP(X2,X1,X4,X5)))
    | ~ order(X2)
    | ~ order(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X4,sk1_esk44_6(X1,X2,X6,X3,X4,X5))),hAPP(X2,X1,X4,sk1_esk45_6(X1,X2,X6,X3,X4,X5)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2814]) ).

cnf(c_0_2814_5,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X2,X1,X4,sk1_esk44_6(X1,X2,X6,X3,X4,X5))),hAPP(X2,X1,X4,sk1_esk45_6(X1,X2,X6,X3,X4,X5))))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X5),X6))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),hAPP(X2,X1,X4,X5)))
    | ~ order(X2)
    | ~ order(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6))) ),
    inference(literals_permutation,[status(thm)],[c_0_2814]) ).

cnf(c_0_2815_0,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk2_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk2_6(X6,X5,X3,X4,X1,X2)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2815]) ).

cnf(c_0_2815_1,axiom,
    ( ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk2_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk2_6(X6,X5,X3,X4,X1,X2)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2815]) ).

cnf(c_0_2815_2,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk2_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk2_6(X6,X5,X3,X4,X1,X2)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2815]) ).

cnf(c_0_2815_3,axiom,
    ( ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk2_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk2_6(X6,X5,X3,X4,X1,X2)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2815]) ).

cnf(c_0_2815_4,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk2_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk2_6(X6,X5,X3,X4,X1,X2)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2815]) ).

cnf(c_0_2815_5,axiom,
    ( ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk2_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk2_6(X6,X5,X3,X4,X1,X2)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2815]) ).

cnf(c_0_2815_6,axiom,
    ( ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk2_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk2_6(X6,X5,X3,X4,X1,X2)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2815]) ).

cnf(c_0_2815_7,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk2_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk2_6(X6,X5,X3,X4,X1,X2)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2815]) ).

cnf(c_0_2815_8,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk2_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk2_6(X6,X5,X3,X4,X1,X2)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2815]) ).

cnf(c_0_2815_9,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk2_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk2_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2815]) ).

cnf(c_0_2816_0,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_2816]) ).

cnf(c_0_2816_1,axiom,
    ( ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_2816]) ).

cnf(c_0_2816_2,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_2816]) ).

cnf(c_0_2816_3,axiom,
    ( ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_2816]) ).

cnf(c_0_2816_4,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_2816]) ).

cnf(c_0_2816_5,axiom,
    ( ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_2816]) ).

cnf(c_0_2816_6,axiom,
    ( ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_2816]) ).

cnf(c_0_2816_7,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_2816]) ).

cnf(c_0_2816_8,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_2816]) ).

cnf(c_0_2816_9,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2816]) ).

cnf(c_0_2817_0,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6))) ),
    inference(literals_permutation,[status(thm)],[c_0_2817]) ).

cnf(c_0_2817_1,axiom,
    ( ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6))) ),
    inference(literals_permutation,[status(thm)],[c_0_2817]) ).

cnf(c_0_2817_2,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6))) ),
    inference(literals_permutation,[status(thm)],[c_0_2817]) ).

cnf(c_0_2817_3,axiom,
    ( ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6))) ),
    inference(literals_permutation,[status(thm)],[c_0_2817]) ).

cnf(c_0_2817_4,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6))) ),
    inference(literals_permutation,[status(thm)],[c_0_2817]) ).

cnf(c_0_2817_5,axiom,
    ( ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6))) ),
    inference(literals_permutation,[status(thm)],[c_0_2817]) ).

cnf(c_0_2817_6,axiom,
    ( ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6))) ),
    inference(literals_permutation,[status(thm)],[c_0_2817]) ).

cnf(c_0_2817_7,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6))) ),
    inference(literals_permutation,[status(thm)],[c_0_2817]) ).

cnf(c_0_2817_8,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6))) ),
    inference(literals_permutation,[status(thm)],[c_0_2817]) ).

cnf(c_0_2817_9,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2817]) ).

cnf(c_0_2818_0,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_2818]) ).

cnf(c_0_2818_1,axiom,
    ( ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_2818]) ).

cnf(c_0_2818_2,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_2818]) ).

cnf(c_0_2818_3,axiom,
    ( ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_2818]) ).

cnf(c_0_2818_4,axiom,
    ( ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_2818]) ).

cnf(c_0_2818_5,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_2818]) ).

cnf(c_0_2818_6,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_2818]) ).

cnf(c_0_2818_7,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2818]) ).

cnf(c_0_2819_0,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6))) ),
    inference(literals_permutation,[status(thm)],[c_0_2819]) ).

cnf(c_0_2819_1,axiom,
    ( ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6))) ),
    inference(literals_permutation,[status(thm)],[c_0_2819]) ).

cnf(c_0_2819_2,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6))) ),
    inference(literals_permutation,[status(thm)],[c_0_2819]) ).

cnf(c_0_2819_3,axiom,
    ( ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6))) ),
    inference(literals_permutation,[status(thm)],[c_0_2819]) ).

cnf(c_0_2819_4,axiom,
    ( ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6))) ),
    inference(literals_permutation,[status(thm)],[c_0_2819]) ).

cnf(c_0_2819_5,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6))) ),
    inference(literals_permutation,[status(thm)],[c_0_2819]) ).

cnf(c_0_2819_6,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6))) ),
    inference(literals_permutation,[status(thm)],[c_0_2819]) ).

cnf(c_0_2819_7,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2819]) ).

cnf(c_0_2820_0,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk2_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk2_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_2820]) ).

cnf(c_0_2820_1,axiom,
    ( ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk2_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk2_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_2820]) ).

cnf(c_0_2820_2,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk2_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk2_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_2820]) ).

cnf(c_0_2820_3,axiom,
    ( ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk2_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk2_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_2820]) ).

cnf(c_0_2820_4,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk2_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk2_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_2820]) ).

cnf(c_0_2820_5,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk2_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk2_6(X6,X5,X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_2820]) ).

cnf(c_0_2820_6,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk2_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk2_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_2820]) ).

cnf(c_0_2820_7,axiom,
    ( ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk2_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk2_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_2820]) ).

cnf(c_0_2820_8,axiom,
    ( ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk2_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk2_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_2820]) ).

cnf(c_0_2820_9,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk2_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk2_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2820]) ).

cnf(c_0_2821_0,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_2821]) ).

cnf(c_0_2821_1,axiom,
    ( ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_2821]) ).

cnf(c_0_2821_2,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_2821]) ).

cnf(c_0_2821_3,axiom,
    ( ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_2821]) ).

cnf(c_0_2821_4,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_2821]) ).

cnf(c_0_2821_5,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_2821]) ).

cnf(c_0_2821_6,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_2821]) ).

cnf(c_0_2821_7,axiom,
    ( ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_2821]) ).

cnf(c_0_2821_8,axiom,
    ( ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_2821]) ).

cnf(c_0_2821_9,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2821]) ).

cnf(c_0_2822_0,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6))) ),
    inference(literals_permutation,[status(thm)],[c_0_2822]) ).

cnf(c_0_2822_1,axiom,
    ( ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6))) ),
    inference(literals_permutation,[status(thm)],[c_0_2822]) ).

cnf(c_0_2822_2,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6))) ),
    inference(literals_permutation,[status(thm)],[c_0_2822]) ).

cnf(c_0_2822_3,axiom,
    ( ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6))) ),
    inference(literals_permutation,[status(thm)],[c_0_2822]) ).

cnf(c_0_2822_4,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6))) ),
    inference(literals_permutation,[status(thm)],[c_0_2822]) ).

cnf(c_0_2822_5,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6))) ),
    inference(literals_permutation,[status(thm)],[c_0_2822]) ).

cnf(c_0_2822_6,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6))) ),
    inference(literals_permutation,[status(thm)],[c_0_2822]) ).

cnf(c_0_2822_7,axiom,
    ( ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6))) ),
    inference(literals_permutation,[status(thm)],[c_0_2822]) ).

cnf(c_0_2822_8,axiom,
    ( ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6))) ),
    inference(literals_permutation,[status(thm)],[c_0_2822]) ).

cnf(c_0_2822_9,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk1_6(X6,X5,X3,X4,X1,X2))))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2822]) ).

cnf(c_0_2823_0,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_2823]) ).

cnf(c_0_2823_1,axiom,
    ( ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_2823]) ).

cnf(c_0_2823_2,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_2823]) ).

cnf(c_0_2823_3,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_2823]) ).

cnf(c_0_2823_4,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_2823]) ).

cnf(c_0_2823_5,axiom,
    ( ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_2823]) ).

cnf(c_0_2823_6,axiom,
    ( ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_2823]) ).

cnf(c_0_2823_7,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2823]) ).

cnf(c_0_2824_0,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6))) ),
    inference(literals_permutation,[status(thm)],[c_0_2824]) ).

cnf(c_0_2824_1,axiom,
    ( ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6))) ),
    inference(literals_permutation,[status(thm)],[c_0_2824]) ).

cnf(c_0_2824_2,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6))) ),
    inference(literals_permutation,[status(thm)],[c_0_2824]) ).

cnf(c_0_2824_3,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6))) ),
    inference(literals_permutation,[status(thm)],[c_0_2824]) ).

cnf(c_0_2824_4,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6))) ),
    inference(literals_permutation,[status(thm)],[c_0_2824]) ).

cnf(c_0_2824_5,axiom,
    ( ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6))) ),
    inference(literals_permutation,[status(thm)],[c_0_2824]) ).

cnf(c_0_2824_6,axiom,
    ( ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6))) ),
    inference(literals_permutation,[status(thm)],[c_0_2824]) ).

cnf(c_0_2824_7,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X6)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X6),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X4)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X6,sk1_esk4_6(X6,X5,X3,X4,X1,X2))))
    | ti(arrow_490897120le_alt,X3) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2824]) ).

cnf(c_0_2825_0,axiom,
    ( hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),X1))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,X2))))) != zero_zero(nat)
    | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_2825]) ).

cnf(c_0_2825_1,axiom,
    ( ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),X1))
    | hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),X1))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,X2))))) != zero_zero(nat) ),
    inference(literals_permutation,[status(thm)],[c_0_2825]) ).

cnf(c_0_2826_0,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2826]) ).

cnf(c_0_2826_1,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2826]) ).

cnf(c_0_2826_2,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2826]) ).

cnf(c_0_2826_3,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2826]) ).

cnf(c_0_2826_4,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab)) ),
    inference(literals_permutation,[status(thm)],[c_0_2826]) ).

cnf(c_0_2827_0,axiom,
    ( hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,X1),X2))
    | ~ hBOOL(hAPP(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1111136790e_Prof),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_2064824852le_Lin))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sk1_esk24_2(X2,X1)),sk1_esk25_2(X2,X1))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,sk1_esk23_2(X2,X1)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2827]) ).

cnf(c_0_2827_1,axiom,
    ( ~ hBOOL(hAPP(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1111136790e_Prof),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_2064824852le_Lin))))
    | hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,X1),X2))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sk1_esk24_2(X2,X1)),sk1_esk25_2(X2,X1))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,sk1_esk23_2(X2,X1)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2827]) ).

cnf(c_0_2827_2,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sk1_esk24_2(X2,X1)),sk1_esk25_2(X2,X1))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,sk1_esk23_2(X2,X1))))
    | ~ hBOOL(hAPP(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1111136790e_Prof),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_2064824852le_Lin))))
    | hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_2827]) ).

cnf(c_0_2828_0,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(literals_permutation,[status(thm)],[c_0_2828]) ).

cnf(c_0_2828_1,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(literals_permutation,[status(thm)],[c_0_2828]) ).

cnf(c_0_2828_2,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(literals_permutation,[status(thm)],[c_0_2828]) ).

cnf(c_0_2828_3,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(literals_permutation,[status(thm)],[c_0_2828]) ).

cnf(c_0_2828_4,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba)) ),
    inference(literals_permutation,[status(thm)],[c_0_2828]) ).

cnf(c_0_2829_0,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2829]) ).

cnf(c_0_2829_1,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2829]) ).

cnf(c_0_2829_2,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2829]) ).

cnf(c_0_2829_3,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2829]) ).

cnf(c_0_2829_4,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab)) ),
    inference(literals_permutation,[status(thm)],[c_0_2829]) ).

cnf(c_0_2830_0,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(literals_permutation,[status(thm)],[c_0_2830]) ).

cnf(c_0_2830_1,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(literals_permutation,[status(thm)],[c_0_2830]) ).

cnf(c_0_2830_2,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(literals_permutation,[status(thm)],[c_0_2830]) ).

cnf(c_0_2830_3,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(literals_permutation,[status(thm)],[c_0_2830]) ).

cnf(c_0_2830_4,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba)) ),
    inference(literals_permutation,[status(thm)],[c_0_2830]) ).

cnf(c_0_2831_0,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(literals_permutation,[status(thm)],[c_0_2831]) ).

cnf(c_0_2831_1,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(literals_permutation,[status(thm)],[c_0_2831]) ).

cnf(c_0_2831_2,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(literals_permutation,[status(thm)],[c_0_2831]) ).

cnf(c_0_2831_3,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_2831]) ).

cnf(c_0_2832_0,axiom,
    ( hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,X1),X2))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sk1_esk24_2(X2,X1)),sk1_esk25_2(X2,X1))),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),sk1_esk23_2(X2,X1),X2)))
    | ~ hBOOL(hAPP(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1111136790e_Prof),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_2064824852le_Lin)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2832]) ).

cnf(c_0_2832_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sk1_esk24_2(X2,X1)),sk1_esk25_2(X2,X1))),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),sk1_esk23_2(X2,X1),X2)))
    | hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,X1),X2))
    | ~ hBOOL(hAPP(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1111136790e_Prof),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_2064824852le_Lin)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2832]) ).

cnf(c_0_2832_2,axiom,
    ( ~ hBOOL(hAPP(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1111136790e_Prof),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_2064824852le_Lin))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sk1_esk24_2(X2,X1)),sk1_esk25_2(X2,X1))),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),sk1_esk23_2(X2,X1),X2)))
    | hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_2832]) ).

cnf(c_0_2833_0,axiom,
    ( hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,X1),X2))
    | hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),sk1_esk23_2(X2,X1)),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1111136790e_Prof),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_2064824852le_Lin)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2833]) ).

cnf(c_0_2833_1,axiom,
    ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),sk1_esk23_2(X2,X1)),arrow_1111136790e_Prof))
    | hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,X1),X2))
    | ~ hBOOL(hAPP(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1111136790e_Prof),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_2064824852le_Lin)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2833]) ).

cnf(c_0_2833_2,axiom,
    ( ~ hBOOL(hAPP(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1111136790e_Prof),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_2064824852le_Lin))))
    | hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),sk1_esk23_2(X2,X1)),arrow_1111136790e_Prof))
    | hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_2833]) ).

cnf(c_0_2834_0,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X3)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X2),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,sk1_esk9_5(X1,X2,X3,X4,X5))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X2,sk1_esk9_5(X1,X2,X3,X4,X5))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_2834]) ).

cnf(c_0_2834_1,axiom,
    ( ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X3)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X2),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,sk1_esk9_5(X1,X2,X3,X4,X5))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X2,sk1_esk9_5(X1,X2,X3,X4,X5))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_2834]) ).

cnf(c_0_2834_2,axiom,
    ( ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X2),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X3)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,sk1_esk9_5(X1,X2,X3,X4,X5))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X2,sk1_esk9_5(X1,X2,X3,X4,X5))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_2834]) ).

cnf(c_0_2834_3,axiom,
    ( ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X2),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X3)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,sk1_esk9_5(X1,X2,X3,X4,X5))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X2,sk1_esk9_5(X1,X2,X3,X4,X5))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_2834]) ).

cnf(c_0_2834_4,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,sk1_esk9_5(X1,X2,X3,X4,X5))))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X2),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X3)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X2,sk1_esk9_5(X1,X2,X3,X4,X5))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_2834]) ).

cnf(c_0_2834_5,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X2,sk1_esk9_5(X1,X2,X3,X4,X5))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,sk1_esk9_5(X1,X2,X3,X4,X5))))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X2),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X3)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_2834]) ).

cnf(c_0_2834_6,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X2)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X2,sk1_esk9_5(X1,X2,X3,X4,X5))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,sk1_esk9_5(X1,X2,X3,X4,X5))))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X2),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_2834]) ).

cnf(c_0_2835_0,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X2)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X2),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,sk1_esk9_5(X1,X2,X3,X4,X5))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X2,sk1_esk9_5(X1,X2,X3,X4,X5))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_2835]) ).

cnf(c_0_2835_1,axiom,
    ( ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X2)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X2),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,sk1_esk9_5(X1,X2,X3,X4,X5))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X2,sk1_esk9_5(X1,X2,X3,X4,X5))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_2835]) ).

cnf(c_0_2835_2,axiom,
    ( ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X2),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X2)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,sk1_esk9_5(X1,X2,X3,X4,X5))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X2,sk1_esk9_5(X1,X2,X3,X4,X5))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_2835]) ).

cnf(c_0_2835_3,axiom,
    ( ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X2),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X2)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,sk1_esk9_5(X1,X2,X3,X4,X5))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X2,sk1_esk9_5(X1,X2,X3,X4,X5))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_2835]) ).

cnf(c_0_2835_4,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,sk1_esk9_5(X1,X2,X3,X4,X5))))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X2),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X2)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X2,sk1_esk9_5(X1,X2,X3,X4,X5))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_2835]) ).

cnf(c_0_2835_5,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X2,sk1_esk9_5(X1,X2,X3,X4,X5))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,sk1_esk9_5(X1,X2,X3,X4,X5))))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X2),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X2)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_2835]) ).

cnf(c_0_2835_6,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X3)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X2,sk1_esk9_5(X1,X2,X3,X4,X5))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,sk1_esk9_5(X1,X2,X3,X4,X5))))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X2),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_2835]) ).

cnf(c_0_2836_0,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_2836]) ).

cnf(c_0_2836_1,axiom,
    ( ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_2836]) ).

cnf(c_0_2836_2,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_2836]) ).

cnf(c_0_2836_3,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_2836]) ).

cnf(c_0_2836_4,axiom,
    ( ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_2836]) ).

cnf(c_0_2836_5,axiom,
    ( ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_2836]) ).

cnf(c_0_2836_6,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_2836]) ).

cnf(c_0_2836_7,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_2836]) ).

cnf(c_0_2836_8,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2836]) ).

cnf(c_0_2837_0,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_2837]) ).

cnf(c_0_2837_1,axiom,
    ( ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_2837]) ).

cnf(c_0_2837_2,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_2837]) ).

cnf(c_0_2837_3,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_2837]) ).

cnf(c_0_2837_4,axiom,
    ( ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_2837]) ).

cnf(c_0_2837_5,axiom,
    ( ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_2837]) ).

cnf(c_0_2837_6,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_2837]) ).

cnf(c_0_2837_7,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_2837]) ).

cnf(c_0_2837_8,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2837]) ).

cnf(c_0_2838_0,axiom,
    ( hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,X1),X2))
    | ~ hBOOL(hAPP(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1111136790e_Prof),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_2064824852le_Lin))))
    | ti(arrow_490897120le_alt,sk1_esk25_2(X2,X1)) != ti(arrow_490897120le_alt,sk1_esk24_2(X2,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_2838]) ).

cnf(c_0_2838_1,axiom,
    ( ~ hBOOL(hAPP(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1111136790e_Prof),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_2064824852le_Lin))))
    | hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,X1),X2))
    | ti(arrow_490897120le_alt,sk1_esk25_2(X2,X1)) != ti(arrow_490897120le_alt,sk1_esk24_2(X2,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_2838]) ).

cnf(c_0_2838_2,axiom,
    ( ti(arrow_490897120le_alt,sk1_esk25_2(X2,X1)) != ti(arrow_490897120le_alt,sk1_esk24_2(X2,X1))
    | ~ hBOOL(hAPP(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X1),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1111136790e_Prof),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_2064824852le_Lin))))
    | hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_2838]) ).

cnf(c_0_2839_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2839]) ).

cnf(c_0_2839_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2839]) ).

cnf(c_0_2839_2,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2839]) ).

cnf(c_0_2839_3,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2839]) ).

cnf(c_0_2839_4,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2839]) ).

cnf(c_0_2840_0,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2840]) ).

cnf(c_0_2840_1,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2840]) ).

cnf(c_0_2840_2,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2840]) ).

cnf(c_0_2840_3,axiom,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2840]) ).

cnf(c_0_2840_4,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab)) ),
    inference(literals_permutation,[status(thm)],[c_0_2840]) ).

cnf(c_0_2841_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fdisj),X2)),X3)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2841]) ).

cnf(c_0_2841_1,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fdisj),X2)),X3))))
    | hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_2841]) ).

cnf(c_0_2842_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X3)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fdisj),X2)),X3)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2842]) ).

cnf(c_0_2842_1,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fdisj),X2)),X3))))
    | hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_2842]) ).

cnf(c_0_2843_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(literals_permutation,[status(thm)],[c_0_2843]) ).

cnf(c_0_2843_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(literals_permutation,[status(thm)],[c_0_2843]) ).

cnf(c_0_2843_2,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(literals_permutation,[status(thm)],[c_0_2843]) ).

cnf(c_0_2843_3,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(literals_permutation,[status(thm)],[c_0_2843]) ).

cnf(c_0_2843_4,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2843]) ).

cnf(c_0_2844_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2844]) ).

cnf(c_0_2844_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2844]) ).

cnf(c_0_2844_2,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2844]) ).

cnf(c_0_2844_3,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2844]) ).

cnf(c_0_2844_4,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2844]) ).

cnf(c_0_2845_0,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2845]) ).

cnf(c_0_2845_1,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2845]) ).

cnf(c_0_2845_2,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2845]) ).

cnf(c_0_2845_3,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2845]) ).

cnf(c_0_2845_4,axiom,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba)) ),
    inference(literals_permutation,[status(thm)],[c_0_2845]) ).

cnf(c_0_2846_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(literals_permutation,[status(thm)],[c_0_2846]) ).

cnf(c_0_2846_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(literals_permutation,[status(thm)],[c_0_2846]) ).

cnf(c_0_2846_2,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(literals_permutation,[status(thm)],[c_0_2846]) ).

cnf(c_0_2846_3,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(literals_permutation,[status(thm)],[c_0_2846]) ).

cnf(c_0_2846_4,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2846]) ).

cnf(c_0_2847_0,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2847]) ).

cnf(c_0_2847_1,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2847]) ).

cnf(c_0_2847_2,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2847]) ).

cnf(c_0_2847_3,axiom,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2847]) ).

cnf(c_0_2847_4,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab)) ),
    inference(literals_permutation,[status(thm)],[c_0_2847]) ).

cnf(c_0_2848_0,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(literals_permutation,[status(thm)],[c_0_2848]) ).

cnf(c_0_2848_1,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(literals_permutation,[status(thm)],[c_0_2848]) ).

cnf(c_0_2848_2,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(literals_permutation,[status(thm)],[c_0_2848]) ).

cnf(c_0_2848_3,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_2848]) ).

cnf(c_0_2849_0,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2849]) ).

cnf(c_0_2849_1,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2849]) ).

cnf(c_0_2849_2,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2849]) ).

cnf(c_0_2849_3,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2849]) ).

cnf(c_0_2849_4,axiom,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba)) ),
    inference(literals_permutation,[status(thm)],[c_0_2849]) ).

cnf(c_0_2850_0,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2850]) ).

cnf(c_0_2850_1,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2850]) ).

cnf(c_0_2850_2,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2850]) ).

cnf(c_0_2850_3,axiom,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_2850]) ).

cnf(c_0_2851_0,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,sk1_esk9_5(X1,X2,X3,X4,X5))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X2,sk1_esk9_5(X1,X2,X3,X4,X5))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X3)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X2),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_2851]) ).

cnf(c_0_2851_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X2,sk1_esk9_5(X1,X2,X3,X4,X5))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,sk1_esk9_5(X1,X2,X3,X4,X5))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X3)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X2),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_2851]) ).

cnf(c_0_2851_2,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X3)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X2,sk1_esk9_5(X1,X2,X3,X4,X5))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,sk1_esk9_5(X1,X2,X3,X4,X5))))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X2),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_2851]) ).

cnf(c_0_2851_3,axiom,
    ( ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X3)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X2,sk1_esk9_5(X1,X2,X3,X4,X5))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,sk1_esk9_5(X1,X2,X3,X4,X5))))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X2),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_2851]) ).

cnf(c_0_2851_4,axiom,
    ( ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X2),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X3)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X2,sk1_esk9_5(X1,X2,X3,X4,X5))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,sk1_esk9_5(X1,X2,X3,X4,X5))))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_2851]) ).

cnf(c_0_2851_5,axiom,
    ( ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X2),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X3)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X2,sk1_esk9_5(X1,X2,X3,X4,X5))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,sk1_esk9_5(X1,X2,X3,X4,X5))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_2851]) ).

cnf(c_0_2851_6,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X2)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X2),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X3)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X2,sk1_esk9_5(X1,X2,X3,X4,X5))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,sk1_esk9_5(X1,X2,X3,X4,X5)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2851]) ).

cnf(c_0_2852_0,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,sk1_esk9_5(X1,X2,X3,X4,X5))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X2,sk1_esk9_5(X1,X2,X3,X4,X5))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X2)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X2),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_2852]) ).

cnf(c_0_2852_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X2,sk1_esk9_5(X1,X2,X3,X4,X5))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,sk1_esk9_5(X1,X2,X3,X4,X5))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X2)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X2),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_2852]) ).

cnf(c_0_2852_2,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X2)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X2,sk1_esk9_5(X1,X2,X3,X4,X5))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,sk1_esk9_5(X1,X2,X3,X4,X5))))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X2),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_2852]) ).

cnf(c_0_2852_3,axiom,
    ( ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X2)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X2,sk1_esk9_5(X1,X2,X3,X4,X5))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,sk1_esk9_5(X1,X2,X3,X4,X5))))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X2),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_2852]) ).

cnf(c_0_2852_4,axiom,
    ( ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X2),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X2)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X2,sk1_esk9_5(X1,X2,X3,X4,X5))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,sk1_esk9_5(X1,X2,X3,X4,X5))))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_2852]) ).

cnf(c_0_2852_5,axiom,
    ( ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X2),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X2)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X2,sk1_esk9_5(X1,X2,X3,X4,X5))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,sk1_esk9_5(X1,X2,X3,X4,X5))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_2852]) ).

cnf(c_0_2852_6,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X3)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X2),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X2)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X2,sk1_esk9_5(X1,X2,X3,X4,X5))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,sk1_esk9_5(X1,X2,X3,X4,X5)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2852]) ).

cnf(c_0_2853_0,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_2853]) ).

cnf(c_0_2853_1,axiom,
    ( ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_2853]) ).

cnf(c_0_2853_2,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_2853]) ).

cnf(c_0_2853_3,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_2853]) ).

cnf(c_0_2853_4,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_2853]) ).

cnf(c_0_2853_5,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_2853]) ).

cnf(c_0_2853_6,axiom,
    ( ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_2853]) ).

cnf(c_0_2853_7,axiom,
    ( ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_2853]) ).

cnf(c_0_2853_8,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2853]) ).

cnf(c_0_2854_0,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_2854]) ).

cnf(c_0_2854_1,axiom,
    ( ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_2854]) ).

cnf(c_0_2854_2,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_2854]) ).

cnf(c_0_2854_3,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_2854]) ).

cnf(c_0_2854_4,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_2854]) ).

cnf(c_0_2854_5,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_2854]) ).

cnf(c_0_2854_6,axiom,
    ( ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_2854]) ).

cnf(c_0_2854_7,axiom,
    ( ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_2854]) ).

cnf(c_0_2854_8,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X5)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X5),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X5,sk1_esk3_5(X5,X4,X3,X1,X2))))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2854]) ).

cnf(c_0_2855_0,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk5_4(X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,sk1_esk5_4(X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_2855]) ).

cnf(c_0_2855_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk5_4(X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,sk1_esk5_4(X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_2855]) ).

cnf(c_0_2855_2,axiom,
    ( ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk5_4(X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,sk1_esk5_4(X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_2855]) ).

cnf(c_0_2855_3,axiom,
    ( ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk5_4(X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,sk1_esk5_4(X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_2855]) ).

cnf(c_0_2855_4,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk5_4(X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,sk1_esk5_4(X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_2855]) ).

cnf(c_0_2855_5,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,sk1_esk5_4(X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk5_4(X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_2855]) ).

cnf(c_0_2855_6,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,sk1_esk5_4(X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk5_4(X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2855]) ).

cnf(c_0_2856_0,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk5_4(X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,sk1_esk5_4(X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_2856]) ).

cnf(c_0_2856_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk5_4(X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,sk1_esk5_4(X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_2856]) ).

cnf(c_0_2856_2,axiom,
    ( ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk5_4(X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,sk1_esk5_4(X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_2856]) ).

cnf(c_0_2856_3,axiom,
    ( ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk5_4(X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,sk1_esk5_4(X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_2856]) ).

cnf(c_0_2856_4,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk5_4(X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,sk1_esk5_4(X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_2856]) ).

cnf(c_0_2856_5,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,sk1_esk5_4(X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk5_4(X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_2856]) ).

cnf(c_0_2856_6,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,sk1_esk5_4(X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk5_4(X4,X3,X1,X2))))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2856]) ).

cnf(c_0_2857_0,axiom,
    ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),sk1_esk58_6(X1,X2,X5,X6,X3,X4)),sk1_esk59_6(X1,X2,X5,X6,X3,X4)))
    | ~ order(X1)
    | ~ order(X2)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X5,X4)),X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_2857]) ).

cnf(c_0_2857_1,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),sk1_esk58_6(X1,X2,X5,X6,X3,X4)),sk1_esk59_6(X1,X2,X5,X6,X3,X4)))
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6))
    | ~ order(X1)
    | ~ order(X2)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X5,X4)),X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_2857]) ).

cnf(c_0_2857_2,axiom,
    ( ~ order(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),sk1_esk58_6(X1,X2,X5,X6,X3,X4)),sk1_esk59_6(X1,X2,X5,X6,X3,X4)))
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6))
    | ~ order(X2)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X5,X4)),X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_2857]) ).

cnf(c_0_2857_3,axiom,
    ( ~ order(X2)
    | ~ order(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),sk1_esk58_6(X1,X2,X5,X6,X3,X4)),sk1_esk59_6(X1,X2,X5,X6,X3,X4)))
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X5,X4)),X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_2857]) ).

cnf(c_0_2857_4,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
    | ~ order(X2)
    | ~ order(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),sk1_esk58_6(X1,X2,X5,X6,X3,X4)),sk1_esk59_6(X1,X2,X5,X6,X3,X4)))
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X5,X4)),X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_2857]) ).

cnf(c_0_2857_5,axiom,
    ( ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X5,X4)),X6))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
    | ~ order(X2)
    | ~ order(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),sk1_esk58_6(X1,X2,X5,X6,X3,X4)),sk1_esk59_6(X1,X2,X5,X6,X3,X4)))
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_2857]) ).

cnf(c_0_2858_0,axiom,
    ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),sk1_esk48_6(X1,X2,X5,X6,X3,X4)),sk1_esk49_6(X1,X2,X5,X6,X3,X4)))
    | ~ order(X1)
    | ~ order(X2)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X4)),X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_2858]) ).

cnf(c_0_2858_1,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),sk1_esk48_6(X1,X2,X5,X6,X3,X4)),sk1_esk49_6(X1,X2,X5,X6,X3,X4)))
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6))
    | ~ order(X1)
    | ~ order(X2)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X4)),X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_2858]) ).

cnf(c_0_2858_2,axiom,
    ( ~ order(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),sk1_esk48_6(X1,X2,X5,X6,X3,X4)),sk1_esk49_6(X1,X2,X5,X6,X3,X4)))
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6))
    | ~ order(X2)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X4)),X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_2858]) ).

cnf(c_0_2858_3,axiom,
    ( ~ order(X2)
    | ~ order(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),sk1_esk48_6(X1,X2,X5,X6,X3,X4)),sk1_esk49_6(X1,X2,X5,X6,X3,X4)))
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X4)),X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_2858]) ).

cnf(c_0_2858_4,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
    | ~ order(X2)
    | ~ order(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),sk1_esk48_6(X1,X2,X5,X6,X3,X4)),sk1_esk49_6(X1,X2,X5,X6,X3,X4)))
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X4)),X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_2858]) ).

cnf(c_0_2858_5,axiom,
    ( ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X4)),X6))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
    | ~ order(X2)
    | ~ order(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),sk1_esk48_6(X1,X2,X5,X6,X3,X4)),sk1_esk49_6(X1,X2,X5,X6,X3,X4)))
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X5,X3)),X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_2858]) ).

cnf(c_0_2859_0,axiom,
    ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),sk1_esk43_6(X1,X2,X6,X3,X4,X5)),sk1_esk42_6(X1,X2,X6,X3,X4,X5)))
    | ~ order(X1)
    | ~ order(X2)
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X4)),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_2859]) ).

cnf(c_0_2859_1,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),sk1_esk43_6(X1,X2,X6,X3,X4,X5)),sk1_esk42_6(X1,X2,X6,X3,X4,X5)))
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5))
    | ~ order(X1)
    | ~ order(X2)
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X4)),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_2859]) ).

cnf(c_0_2859_2,axiom,
    ( ~ order(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),sk1_esk43_6(X1,X2,X6,X3,X4,X5)),sk1_esk42_6(X1,X2,X6,X3,X4,X5)))
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5))
    | ~ order(X2)
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X4)),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_2859]) ).

cnf(c_0_2859_3,axiom,
    ( ~ order(X2)
    | ~ order(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),sk1_esk43_6(X1,X2,X6,X3,X4,X5)),sk1_esk42_6(X1,X2,X6,X3,X4,X5)))
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X4)),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_2859]) ).

cnf(c_0_2859_4,axiom,
    ( ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X4)),X5))
    | ~ order(X2)
    | ~ order(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),sk1_esk43_6(X1,X2,X6,X3,X4,X5)),sk1_esk42_6(X1,X2,X6,X3,X4,X5)))
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_2859]) ).

cnf(c_0_2859_5,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X6),X4))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X4)),X5))
    | ~ order(X2)
    | ~ order(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),sk1_esk43_6(X1,X2,X6,X3,X4,X5)),sk1_esk42_6(X1,X2,X6,X3,X4,X5)))
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_2859]) ).

cnf(c_0_2860_0,axiom,
    ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),sk1_esk41_6(X1,X2,X6,X3,X4,X5)),sk1_esk40_6(X1,X2,X6,X3,X4,X5)))
    | ~ ord(X1)
    | ~ order(X2)
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,X4)),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_2860]) ).

cnf(c_0_2860_1,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),sk1_esk41_6(X1,X2,X6,X3,X4,X5)),sk1_esk40_6(X1,X2,X6,X3,X4,X5)))
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5))
    | ~ ord(X1)
    | ~ order(X2)
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,X4)),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_2860]) ).

cnf(c_0_2860_2,axiom,
    ( ~ ord(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),sk1_esk41_6(X1,X2,X6,X3,X4,X5)),sk1_esk40_6(X1,X2,X6,X3,X4,X5)))
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5))
    | ~ order(X2)
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,X4)),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_2860]) ).

cnf(c_0_2860_3,axiom,
    ( ~ order(X2)
    | ~ ord(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),sk1_esk41_6(X1,X2,X6,X3,X4,X5)),sk1_esk40_6(X1,X2,X6,X3,X4,X5)))
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,X4)),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_2860]) ).

cnf(c_0_2860_4,axiom,
    ( ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,X4)),X5))
    | ~ order(X2)
    | ~ ord(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),sk1_esk41_6(X1,X2,X6,X3,X4,X5)),sk1_esk40_6(X1,X2,X6,X3,X4,X5)))
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_2860]) ).

cnf(c_0_2860_5,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X4))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,X4)),X5))
    | ~ order(X2)
    | ~ ord(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),sk1_esk41_6(X1,X2,X6,X3,X4,X5)),sk1_esk40_6(X1,X2,X6,X3,X4,X5)))
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),hAPP(X1,X2,X3,X6)),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_2860]) ).

cnf(c_0_2862_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4)))
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),sk1_esk57_6(X1,X2,X5,X6,X3,X4)),sk1_esk56_6(X1,X2,X5,X6,X3,X4)))
    | ~ order(X1)
    | ~ order(X2)
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X3),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_2862]) ).

cnf(c_0_2862_1,axiom,
    ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),sk1_esk57_6(X1,X2,X5,X6,X3,X4)),sk1_esk56_6(X1,X2,X5,X6,X3,X4)))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4)))
    | ~ order(X1)
    | ~ order(X2)
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X3),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_2862]) ).

cnf(c_0_2862_2,axiom,
    ( ~ order(X1)
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),sk1_esk57_6(X1,X2,X5,X6,X3,X4)),sk1_esk56_6(X1,X2,X5,X6,X3,X4)))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4)))
    | ~ order(X2)
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X3),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_2862]) ).

cnf(c_0_2862_3,axiom,
    ( ~ order(X2)
    | ~ order(X1)
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),sk1_esk57_6(X1,X2,X5,X6,X3,X4)),sk1_esk56_6(X1,X2,X5,X6,X3,X4)))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4)))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X3),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_2862]) ).

cnf(c_0_2862_4,axiom,
    ( ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X3),X4))
    | ~ order(X2)
    | ~ order(X1)
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),sk1_esk57_6(X1,X2,X5,X6,X3,X4)),sk1_esk56_6(X1,X2,X5,X6,X3,X4)))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_2862]) ).

cnf(c_0_2862_5,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X3)))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X3),X4))
    | ~ order(X2)
    | ~ order(X1)
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),sk1_esk57_6(X1,X2,X5,X6,X3,X4)),sk1_esk56_6(X1,X2,X5,X6,X3,X4)))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_2862]) ).

cnf(c_0_2863_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4)))
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),sk1_esk55_6(X1,X2,X5,X6,X3,X4)),sk1_esk54_6(X1,X2,X5,X6,X3,X4)))
    | ~ order(X1)
    | ~ order(X2)
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X3),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),hAPP(X2,X1,X6,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_2863]) ).

cnf(c_0_2863_1,axiom,
    ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),sk1_esk55_6(X1,X2,X5,X6,X3,X4)),sk1_esk54_6(X1,X2,X5,X6,X3,X4)))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4)))
    | ~ order(X1)
    | ~ order(X2)
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X3),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),hAPP(X2,X1,X6,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_2863]) ).

cnf(c_0_2863_2,axiom,
    ( ~ order(X1)
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),sk1_esk55_6(X1,X2,X5,X6,X3,X4)),sk1_esk54_6(X1,X2,X5,X6,X3,X4)))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4)))
    | ~ order(X2)
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X3),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),hAPP(X2,X1,X6,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_2863]) ).

cnf(c_0_2863_3,axiom,
    ( ~ order(X2)
    | ~ order(X1)
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),sk1_esk55_6(X1,X2,X5,X6,X3,X4)),sk1_esk54_6(X1,X2,X5,X6,X3,X4)))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4)))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X3),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),hAPP(X2,X1,X6,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_2863]) ).

cnf(c_0_2863_4,axiom,
    ( ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X3),X4))
    | ~ order(X2)
    | ~ order(X1)
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),sk1_esk55_6(X1,X2,X5,X6,X3,X4)),sk1_esk54_6(X1,X2,X5,X6,X3,X4)))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),hAPP(X2,X1,X6,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_2863]) ).

cnf(c_0_2863_5,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X5),hAPP(X2,X1,X6,X3)))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X3),X4))
    | ~ order(X2)
    | ~ order(X1)
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),sk1_esk55_6(X1,X2,X5,X6,X3,X4)),sk1_esk54_6(X1,X2,X5,X6,X3,X4)))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),hAPP(X2,X1,X6,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_2863]) ).

cnf(c_0_2864_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6)))
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),sk1_esk46_6(X1,X2,X6,X3,X4,X5)),sk1_esk47_6(X1,X2,X6,X3,X4,X5)))
    | ~ order(X1)
    | ~ order(X2)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X5)))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X5),X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_2864]) ).

cnf(c_0_2864_1,axiom,
    ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),sk1_esk46_6(X1,X2,X6,X3,X4,X5)),sk1_esk47_6(X1,X2,X6,X3,X4,X5)))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6)))
    | ~ order(X1)
    | ~ order(X2)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X5)))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X5),X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_2864]) ).

cnf(c_0_2864_2,axiom,
    ( ~ order(X1)
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),sk1_esk46_6(X1,X2,X6,X3,X4,X5)),sk1_esk47_6(X1,X2,X6,X3,X4,X5)))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6)))
    | ~ order(X2)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X5)))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X5),X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_2864]) ).

cnf(c_0_2864_3,axiom,
    ( ~ order(X2)
    | ~ order(X1)
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),sk1_esk46_6(X1,X2,X6,X3,X4,X5)),sk1_esk47_6(X1,X2,X6,X3,X4,X5)))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X5)))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X5),X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_2864]) ).

cnf(c_0_2864_4,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X5)))
    | ~ order(X2)
    | ~ order(X1)
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),sk1_esk46_6(X1,X2,X6,X3,X4,X5)),sk1_esk47_6(X1,X2,X6,X3,X4,X5)))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6)))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X5),X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_2864]) ).

cnf(c_0_2864_5,axiom,
    ( ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),X5),X6))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X5)))
    | ~ order(X2)
    | ~ order(X1)
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),sk1_esk46_6(X1,X2,X6,X3,X4,X5)),sk1_esk47_6(X1,X2,X6,X3,X4,X5)))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6))) ),
    inference(literals_permutation,[status(thm)],[c_0_2864]) ).

cnf(c_0_2865_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6)))
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),sk1_esk44_6(X1,X2,X6,X3,X4,X5)),sk1_esk45_6(X1,X2,X6,X3,X4,X5)))
    | ~ order(X1)
    | ~ order(X2)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),hAPP(X2,X1,X4,X5)))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X5),X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_2865]) ).

cnf(c_0_2865_1,axiom,
    ( hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),sk1_esk44_6(X1,X2,X6,X3,X4,X5)),sk1_esk45_6(X1,X2,X6,X3,X4,X5)))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6)))
    | ~ order(X1)
    | ~ order(X2)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),hAPP(X2,X1,X4,X5)))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X5),X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_2865]) ).

cnf(c_0_2865_2,axiom,
    ( ~ order(X1)
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),sk1_esk44_6(X1,X2,X6,X3,X4,X5)),sk1_esk45_6(X1,X2,X6,X3,X4,X5)))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6)))
    | ~ order(X2)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),hAPP(X2,X1,X4,X5)))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X5),X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_2865]) ).

cnf(c_0_2865_3,axiom,
    ( ~ order(X2)
    | ~ order(X1)
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),sk1_esk44_6(X1,X2,X6,X3,X4,X5)),sk1_esk45_6(X1,X2,X6,X3,X4,X5)))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),hAPP(X2,X1,X4,X5)))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X5),X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_2865]) ).

cnf(c_0_2865_4,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),hAPP(X2,X1,X4,X5)))
    | ~ order(X2)
    | ~ order(X1)
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),sk1_esk44_6(X1,X2,X6,X3,X4,X5)),sk1_esk45_6(X1,X2,X6,X3,X4,X5)))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6)))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X5),X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_2865]) ).

cnf(c_0_2865_5,axiom,
    ( ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X5),X6))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),hAPP(X2,X1,X4,X5)))
    | ~ order(X2)
    | ~ order(X1)
    | hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),sk1_esk44_6(X1,X2,X6,X3,X4,X5)),sk1_esk45_6(X1,X2,X6,X3,X4,X5)))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),hAPP(X2,X1,X4,X6))) ),
    inference(literals_permutation,[status(thm)],[c_0_2865]) ).

cnf(c_0_2866_0,axiom,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2866]) ).

cnf(c_0_2866_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2866]) ).

cnf(c_0_2866_2,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2866]) ).

cnf(c_0_2866_3,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2866]) ).

cnf(c_0_2866_4,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n ),
    inference(literals_permutation,[status(thm)],[c_0_2866]) ).

cnf(c_0_2867_0,axiom,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(literals_permutation,[status(thm)],[c_0_2867]) ).

cnf(c_0_2867_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(literals_permutation,[status(thm)],[c_0_2867]) ).

cnf(c_0_2867_2,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(literals_permutation,[status(thm)],[c_0_2867]) ).

cnf(c_0_2867_3,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(literals_permutation,[status(thm)],[c_0_2867]) ).

cnf(c_0_2867_4,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n ),
    inference(literals_permutation,[status(thm)],[c_0_2867]) ).

cnf(c_0_2868_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2868]) ).

cnf(c_0_2868_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2868]) ).

cnf(c_0_2868_2,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2868]) ).

cnf(c_0_2868_3,axiom,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2868]) ).

cnf(c_0_2868_4,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2868]) ).

cnf(c_0_2869_0,axiom,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2869]) ).

cnf(c_0_2869_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2869]) ).

cnf(c_0_2869_2,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2869]) ).

cnf(c_0_2869_3,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2869]) ).

cnf(c_0_2869_4,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n ),
    inference(literals_permutation,[status(thm)],[c_0_2869]) ).

cnf(c_0_2870_0,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk5_4(X4,X3,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,sk1_esk5_4(X4,X3,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_2870]) ).

cnf(c_0_2870_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk5_4(X4,X3,X1,X2))))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,sk1_esk5_4(X4,X3,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_2870]) ).

cnf(c_0_2870_2,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,sk1_esk5_4(X4,X3,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk5_4(X4,X3,X1,X2))))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_2870]) ).

cnf(c_0_2870_3,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,sk1_esk5_4(X4,X3,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk5_4(X4,X3,X1,X2))))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_2870]) ).

cnf(c_0_2870_4,axiom,
    ( ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,sk1_esk5_4(X4,X3,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk5_4(X4,X3,X1,X2))))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_2870]) ).

cnf(c_0_2870_5,axiom,
    ( ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,sk1_esk5_4(X4,X3,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk5_4(X4,X3,X1,X2))))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_2870]) ).

cnf(c_0_2870_6,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,sk1_esk5_4(X4,X3,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk5_4(X4,X3,X1,X2))))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2870]) ).

cnf(c_0_2871_0,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk5_4(X4,X3,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,sk1_esk5_4(X4,X3,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_2871]) ).

cnf(c_0_2871_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk5_4(X4,X3,X1,X2))))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,sk1_esk5_4(X4,X3,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_2871]) ).

cnf(c_0_2871_2,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,sk1_esk5_4(X4,X3,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk5_4(X4,X3,X1,X2))))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_2871]) ).

cnf(c_0_2871_3,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,sk1_esk5_4(X4,X3,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk5_4(X4,X3,X1,X2))))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_2871]) ).

cnf(c_0_2871_4,axiom,
    ( ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,sk1_esk5_4(X4,X3,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk5_4(X4,X3,X1,X2))))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_2871]) ).

cnf(c_0_2871_5,axiom,
    ( ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,sk1_esk5_4(X4,X3,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk5_4(X4,X3,X1,X2))))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_2871]) ).

cnf(c_0_2871_6,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X4)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X3),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,X3)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,sk1_esk5_4(X4,X3,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk5_4(X4,X3,X1,X2))))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2871]) ).

cnf(c_0_2872_0,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X5)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2872]) ).

cnf(c_0_2872_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X5)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2872]) ).

cnf(c_0_2872_2,axiom,
    ( ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X5)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2872]) ).

cnf(c_0_2872_3,axiom,
    ( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X5)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2872]) ).

cnf(c_0_2872_4,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X5)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2872]) ).

cnf(c_0_2872_5,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X5)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2872]) ).

cnf(c_0_2872_6,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X5)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2872]) ).

cnf(c_0_2873_0,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X1)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2873]) ).

cnf(c_0_2873_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X1)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2873]) ).

cnf(c_0_2873_2,axiom,
    ( ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X1)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2873]) ).

cnf(c_0_2873_3,axiom,
    ( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X1)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2873]) ).

cnf(c_0_2873_4,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X1)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2873]) ).

cnf(c_0_2873_5,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X1)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2873]) ).

cnf(c_0_2873_6,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X1)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2873]) ).

cnf(c_0_2874_0,axiom,
    ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(fun(X1,X2),bool),fun(fun(fun(X1,X2),bool),bool),ord_less_eq(fun(fun(X1,X2),bool)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X3),X4)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X3),X5)))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),hAPP(X1,fun(X2,bool),X4,sk1_esk52_5(X2,X1,X4,X5,X3))),hAPP(X1,fun(X2,bool),X5,sk1_esk52_5(X2,X1,X4,X5,X3)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2874]) ).

cnf(c_0_2874_1,axiom,
    ( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),hAPP(X1,fun(X2,bool),X4,sk1_esk52_5(X2,X1,X4,X5,X3))),hAPP(X1,fun(X2,bool),X5,sk1_esk52_5(X2,X1,X4,X5,X3))))
    | hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(fun(X1,X2),bool),fun(fun(fun(X1,X2),bool),bool),ord_less_eq(fun(fun(X1,X2),bool)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X3),X4)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X3),X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_2874]) ).

cnf(c_0_2875_0,axiom,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(literals_permutation,[status(thm)],[c_0_2875]) ).

cnf(c_0_2875_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(literals_permutation,[status(thm)],[c_0_2875]) ).

cnf(c_0_2875_2,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(literals_permutation,[status(thm)],[c_0_2875]) ).

cnf(c_0_2875_3,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(literals_permutation,[status(thm)],[c_0_2875]) ).

cnf(c_0_2875_4,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n ),
    inference(literals_permutation,[status(thm)],[c_0_2875]) ).

cnf(c_0_2876_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2876]) ).

cnf(c_0_2876_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2876]) ).

cnf(c_0_2876_2,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2876]) ).

cnf(c_0_2876_3,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2876]) ).

cnf(c_0_2876_4,axiom,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2876]) ).

cnf(c_0_2877_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk67_6(X2,X1,X3,X4,X5,X6)),X6))
    | hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X5),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X6),X3)))
    | ~ hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X4),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X6),X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_2877]) ).

cnf(c_0_2877_1,axiom,
    ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X5),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X6),X3)))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk67_6(X2,X1,X3,X4,X5,X6)),X6))
    | ~ hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X4),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X6),X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_2877]) ).

cnf(c_0_2877_2,axiom,
    ( ~ hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X4),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X6),X3)))
    | hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X5),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X6),X3)))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk67_6(X2,X1,X3,X4,X5,X6)),X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_2877]) ).

cnf(c_0_2878_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk67_6(X2,X1,X3,X4,X5,X6)),X6))
    | hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X4),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X6),X3)))
    | ~ hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X5),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X6),X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_2878]) ).

cnf(c_0_2878_1,axiom,
    ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X4),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X6),X3)))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk67_6(X2,X1,X3,X4,X5,X6)),X6))
    | ~ hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X5),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X6),X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_2878]) ).

cnf(c_0_2878_2,axiom,
    ( ~ hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X5),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X6),X3)))
    | hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X4),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X6),X3)))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk67_6(X2,X1,X3,X4,X5,X6)),X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_2878]) ).

cnf(c_0_2879_0,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(literals_permutation,[status(thm)],[c_0_2879]) ).

cnf(c_0_2879_1,axiom,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(literals_permutation,[status(thm)],[c_0_2879]) ).

cnf(c_0_2879_2,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(literals_permutation,[status(thm)],[c_0_2879]) ).

cnf(c_0_2879_3,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_2879]) ).

cnf(c_0_2880_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2880]) ).

cnf(c_0_2880_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2880]) ).

cnf(c_0_2880_2,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2880]) ).

cnf(c_0_2880_3,axiom,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2880]) ).

cnf(c_0_2880_4,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2880]) ).

cnf(c_0_2881_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fdisj),X2)),X3))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X3)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_2881]) ).

cnf(c_0_2881_1,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X3)))
    | hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fdisj),X2)),X3))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_2881]) ).

cnf(c_0_2881_2,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X3)))
    | hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fdisj),X2)),X3)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2881]) ).

cnf(c_0_2882_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2882]) ).

cnf(c_0_2882_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2882]) ).

cnf(c_0_2882_2,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2882]) ).

cnf(c_0_2882_3,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2882]) ).

cnf(c_0_2882_4,axiom,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2882]) ).

cnf(c_0_2883_0,axiom,
    ( ti(fun(product_prod(X1,X2),bool),X3) = ti(fun(product_prod(X1,X2),bool),X4)
    | ~ hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),member(product_prod(X1,X2)),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),sk1_esk21_4(X1,X2,X4,X3)),sk1_esk22_4(X1,X2,X4,X3))),X4))
    | ~ hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),member(product_prod(X1,X2)),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),sk1_esk21_4(X1,X2,X4,X3)),sk1_esk22_4(X1,X2,X4,X3))),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2883]) ).

cnf(c_0_2883_1,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),member(product_prod(X1,X2)),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),sk1_esk21_4(X1,X2,X4,X3)),sk1_esk22_4(X1,X2,X4,X3))),X4))
    | ti(fun(product_prod(X1,X2),bool),X3) = ti(fun(product_prod(X1,X2),bool),X4)
    | ~ hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),member(product_prod(X1,X2)),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),sk1_esk21_4(X1,X2,X4,X3)),sk1_esk22_4(X1,X2,X4,X3))),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2883]) ).

cnf(c_0_2883_2,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),member(product_prod(X1,X2)),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),sk1_esk21_4(X1,X2,X4,X3)),sk1_esk22_4(X1,X2,X4,X3))),X3))
    | ~ hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),member(product_prod(X1,X2)),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),sk1_esk21_4(X1,X2,X4,X3)),sk1_esk22_4(X1,X2,X4,X3))),X4))
    | ti(fun(product_prod(X1,X2),bool),X3) = ti(fun(product_prod(X1,X2),bool),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2883]) ).

cnf(c_0_2885_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2885]) ).

cnf(c_0_2885_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2885]) ).

cnf(c_0_2885_2,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2885]) ).

cnf(c_0_2885_3,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2885]) ).

cnf(c_0_2885_4,axiom,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2885]) ).

cnf(c_0_2886_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2886]) ).

cnf(c_0_2886_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2886]) ).

cnf(c_0_2886_2,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2886]) ).

cnf(c_0_2886_3,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2886]) ).

cnf(c_0_2886_4,axiom,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2886]) ).

cnf(c_0_2887_0,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2887]) ).

cnf(c_0_2887_1,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2887]) ).

cnf(c_0_2887_2,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2887]) ).

cnf(c_0_2887_3,axiom,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_2887]) ).

cnf(c_0_2888_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X2)),X3))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_2888]) ).

cnf(c_0_2888_1,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2)))
    | hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X2)),X3)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2888]) ).

cnf(c_0_2889_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X2)),X3))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_2889]) ).

cnf(c_0_2889_1,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X3)))
    | hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(bool,bool)),fun(fun(X1,bool),fun(X1,bool)),combs(X1,bool,bool),hAPP(fun(X1,bool),fun(X1,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X1,bool),fun(X1,fun(bool,bool))),combb(bool,fun(bool,bool),X1),fconj),X2)),X3)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2889]) ).

cnf(c_0_2890_0,axiom,
    ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less_eq(nat)),X1)),X2))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sk1_esk77_2(X2,X1)),hAPP(nat,nat,X1,sk1_esk77_2(X2,X1)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2890]) ).

cnf(c_0_2890_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sk1_esk77_2(X2,X1)),hAPP(nat,nat,X1,sk1_esk77_2(X2,X1))))
    | hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less_eq(nat)),X1)),X2)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2890]) ).

cnf(c_0_2891_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2891]) ).

cnf(c_0_2891_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2891]) ).

cnf(c_0_2891_2,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2891]) ).

cnf(c_0_2891_3,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2891]) ).

cnf(c_0_2891_4,axiom,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2891]) ).

cnf(c_0_2892_0,axiom,
    ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X3),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X4),X5)))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X3,sk1_esk68_5(X2,X1,X3,X5,X4))),hAPP(X1,fun(X2,bool),X5,sk1_esk68_5(X2,X1,X3,X5,X4)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2892]) ).

cnf(c_0_2892_1,axiom,
    ( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X3,sk1_esk68_5(X2,X1,X3,X5,X4))),hAPP(X1,fun(X2,bool),X5,sk1_esk68_5(X2,X1,X3,X5,X4))))
    | hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X3),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X4),X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_2892]) ).

cnf(c_0_2893_0,axiom,
    ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X3),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X4),X5)))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X3,sk1_esk33_5(X2,X1,X3,X5,X4))),hAPP(X1,fun(X2,bool),X5,sk1_esk33_5(X2,X1,X3,X5,X4)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2893]) ).

cnf(c_0_2893_1,axiom,
    ( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X3,sk1_esk33_5(X2,X1,X3,X5,X4))),hAPP(X1,fun(X2,bool),X5,sk1_esk33_5(X2,X1,X3,X5,X4))))
    | hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X3),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X4),X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_2893]) ).

cnf(c_0_2894_0,axiom,
    ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X5),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X6),X4)))
    | hAPP(X1,X2,X3,sk1_esk67_6(X2,X1,X4,X3,X5,X6)) != hAPP(X1,X2,X5,sk1_esk67_6(X2,X1,X4,X3,X5,X6))
    | ~ hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X3),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X6),X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_2894]) ).

cnf(c_0_2894_1,axiom,
    ( hAPP(X1,X2,X3,sk1_esk67_6(X2,X1,X4,X3,X5,X6)) != hAPP(X1,X2,X5,sk1_esk67_6(X2,X1,X4,X3,X5,X6))
    | hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X5),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X6),X4)))
    | ~ hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X3),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X6),X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_2894]) ).

cnf(c_0_2894_2,axiom,
    ( ~ hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X3),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X6),X4)))
    | hAPP(X1,X2,X3,sk1_esk67_6(X2,X1,X4,X3,X5,X6)) != hAPP(X1,X2,X5,sk1_esk67_6(X2,X1,X4,X3,X5,X6))
    | hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X5),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X6),X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_2894]) ).

cnf(c_0_2895_0,axiom,
    ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X3),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X6),X4)))
    | hAPP(X1,X2,X3,sk1_esk67_6(X2,X1,X4,X3,X5,X6)) != hAPP(X1,X2,X5,sk1_esk67_6(X2,X1,X4,X3,X5,X6))
    | ~ hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X5),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X6),X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_2895]) ).

cnf(c_0_2895_1,axiom,
    ( hAPP(X1,X2,X3,sk1_esk67_6(X2,X1,X4,X3,X5,X6)) != hAPP(X1,X2,X5,sk1_esk67_6(X2,X1,X4,X3,X5,X6))
    | hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X3),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X6),X4)))
    | ~ hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X5),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X6),X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_2895]) ).

cnf(c_0_2895_2,axiom,
    ( ~ hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X5),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X6),X4)))
    | hAPP(X1,X2,X3,sk1_esk67_6(X2,X1,X4,X3,X5,X6)) != hAPP(X1,X2,X5,sk1_esk67_6(X2,X1,X4,X3,X5,X6))
    | hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X3),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X6),X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_2895]) ).

cnf(c_0_2896_0,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2896]) ).

cnf(c_0_2896_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2896]) ).

cnf(c_0_2896_2,axiom,
    ( ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2896]) ).

cnf(c_0_2896_3,axiom,
    ( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2896]) ).

cnf(c_0_2896_4,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2896]) ).

cnf(c_0_2896_5,axiom,
    ( ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2896]) ).

cnf(c_0_2896_6,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2896]) ).

cnf(c_0_2897_0,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X5)),X3))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2897]) ).

cnf(c_0_2897_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X5)),X3))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2897]) ).

cnf(c_0_2897_2,axiom,
    ( ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X5)),X3))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2897]) ).

cnf(c_0_2897_3,axiom,
    ( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X5)),X3))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2897]) ).

cnf(c_0_2897_4,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X5)),X3))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2897]) ).

cnf(c_0_2897_5,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X5)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2897]) ).

cnf(c_0_2897_6,axiom,
    ( ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X5)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2897]) ).

cnf(c_0_2898_0,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2898]) ).

cnf(c_0_2898_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2898]) ).

cnf(c_0_2898_2,axiom,
    ( ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2898]) ).

cnf(c_0_2898_3,axiom,
    ( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2898]) ).

cnf(c_0_2898_4,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2898]) ).

cnf(c_0_2898_5,axiom,
    ( ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2898]) ).

cnf(c_0_2898_6,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2898]) ).

cnf(c_0_2899_0,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X1)),X3))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2899]) ).

cnf(c_0_2899_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X1)),X3))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2899]) ).

cnf(c_0_2899_2,axiom,
    ( ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X1)),X3))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2899]) ).

cnf(c_0_2899_3,axiom,
    ( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X1)),X3))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2899]) ).

cnf(c_0_2899_4,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X1)),X3))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2899]) ).

cnf(c_0_2899_5,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X1)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2899]) ).

cnf(c_0_2899_6,axiom,
    ( ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X1)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2899]) ).

cnf(c_0_2900_0,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X5)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2900]) ).

cnf(c_0_2900_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X5)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2900]) ).

cnf(c_0_2900_2,axiom,
    ( ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X5)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2900]) ).

cnf(c_0_2900_3,axiom,
    ( ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X5)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2900]) ).

cnf(c_0_2900_4,axiom,
    ( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X5)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2900]) ).

cnf(c_0_2900_5,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X5)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2900]) ).

cnf(c_0_2900_6,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X5)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2900]) ).

cnf(c_0_2901_0,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2901]) ).

cnf(c_0_2901_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2901]) ).

cnf(c_0_2901_2,axiom,
    ( ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2901]) ).

cnf(c_0_2901_3,axiom,
    ( ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2901]) ).

cnf(c_0_2901_4,axiom,
    ( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2901]) ).

cnf(c_0_2901_5,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2901]) ).

cnf(c_0_2901_6,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2901]) ).

cnf(c_0_2902_0,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X1)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2902]) ).

cnf(c_0_2902_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X1)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2902]) ).

cnf(c_0_2902_2,axiom,
    ( ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X1)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2902]) ).

cnf(c_0_2902_3,axiom,
    ( ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X1)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2902]) ).

cnf(c_0_2902_4,axiom,
    ( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X1)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2902]) ).

cnf(c_0_2902_5,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X1)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2902]) ).

cnf(c_0_2902_6,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X1)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2902]) ).

cnf(c_0_2903_0,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2903]) ).

cnf(c_0_2903_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2903]) ).

cnf(c_0_2903_2,axiom,
    ( ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2903]) ).

cnf(c_0_2903_3,axiom,
    ( ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2903]) ).

cnf(c_0_2903_4,axiom,
    ( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2903]) ).

cnf(c_0_2903_5,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2903]) ).

cnf(c_0_2903_6,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2903]) ).

cnf(c_0_2904_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2904]) ).

cnf(c_0_2904_1,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2904]) ).

cnf(c_0_2904_2,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2904]) ).

cnf(c_0_2904_3,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2904]) ).

cnf(c_0_2904_4,axiom,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2904]) ).

cnf(c_0_2905_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2905]) ).

cnf(c_0_2905_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2905]) ).

cnf(c_0_2905_2,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2905]) ).

cnf(c_0_2905_3,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2905]) ).

cnf(c_0_2905_4,axiom,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2905]) ).

cnf(c_0_2906_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
    | ~ linordered_idom(X1)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),ring_1_Ints(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),one_one(X1)),X2)),X2)),zero_zero(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_2906]) ).

cnf(c_0_2906_1,axiom,
    ( ~ linordered_idom(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),ring_1_Ints(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),one_one(X1)),X2)),X2)),zero_zero(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_2906]) ).

cnf(c_0_2906_2,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),ring_1_Ints(X1)))
    | ~ linordered_idom(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),one_one(X1)),X2)),X2)),zero_zero(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_2906]) ).

cnf(c_0_2906_3,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),one_one(X1)),X2)),X2)),zero_zero(X1)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),ring_1_Ints(X1)))
    | ~ linordered_idom(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_2906]) ).

cnf(c_0_2907_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2907]) ).

cnf(c_0_2907_1,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2907]) ).

cnf(c_0_2907_2,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2907]) ).

cnf(c_0_2907_3,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2907]) ).

cnf(c_0_2907_4,axiom,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2907]) ).

cnf(c_0_2908_0,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2908]) ).

cnf(c_0_2908_1,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2908]) ).

cnf(c_0_2908_2,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2908]) ).

cnf(c_0_2908_3,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab)) ),
    inference(literals_permutation,[status(thm)],[c_0_2908]) ).

cnf(c_0_2909_0,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2909]) ).

cnf(c_0_2909_1,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2909]) ).

cnf(c_0_2909_2,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2909]) ).

cnf(c_0_2909_3,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(literals_permutation,[status(thm)],[c_0_2909]) ).

cnf(c_0_2910_0,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2910]) ).

cnf(c_0_2910_1,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2910]) ).

cnf(c_0_2910_2,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2910]) ).

cnf(c_0_2910_3,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(literals_permutation,[status(thm)],[c_0_2910]) ).

cnf(c_0_2911_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2911]) ).

cnf(c_0_2911_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2911]) ).

cnf(c_0_2911_2,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2911]) ).

cnf(c_0_2911_3,axiom,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2911]) ).

cnf(c_0_2912_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2912]) ).

cnf(c_0_2912_1,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2912]) ).

cnf(c_0_2912_2,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2912]) ).

cnf(c_0_2912_3,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2912]) ).

cnf(c_0_2912_4,axiom,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2912]) ).

cnf(c_0_2913_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2913]) ).

cnf(c_0_2913_1,axiom,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2913]) ).

cnf(c_0_2913_2,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2913]) ).

cnf(c_0_2913_3,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2913]) ).

cnf(c_0_2913_4,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2913]) ).

cnf(c_0_2914_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba)) ),
    inference(literals_permutation,[status(thm)],[c_0_2914]) ).

cnf(c_0_2914_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba)) ),
    inference(literals_permutation,[status(thm)],[c_0_2914]) ).

cnf(c_0_2914_2,axiom,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba)) ),
    inference(literals_permutation,[status(thm)],[c_0_2914]) ).

cnf(c_0_2914_3,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba)) ),
    inference(literals_permutation,[status(thm)],[c_0_2914]) ).

cnf(c_0_2914_4,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2914]) ).

cnf(c_0_2915_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba)) ),
    inference(literals_permutation,[status(thm)],[c_0_2915]) ).

cnf(c_0_2915_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba)) ),
    inference(literals_permutation,[status(thm)],[c_0_2915]) ).

cnf(c_0_2915_2,axiom,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba)) ),
    inference(literals_permutation,[status(thm)],[c_0_2915]) ).

cnf(c_0_2915_3,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba)) ),
    inference(literals_permutation,[status(thm)],[c_0_2915]) ).

cnf(c_0_2915_4,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2915]) ).

cnf(c_0_2916_0,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X5)),X3))
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2916]) ).

cnf(c_0_2916_1,axiom,
    ( ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X5)),X3))
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2916]) ).

cnf(c_0_2916_2,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X5)),X3))
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2916]) ).

cnf(c_0_2916_3,axiom,
    ( ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X5)),X3))
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2916]) ).

cnf(c_0_2916_4,axiom,
    ( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X5)),X3))
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2916]) ).

cnf(c_0_2916_5,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X5)),X3))
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2916]) ).

cnf(c_0_2916_6,axiom,
    ( ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X5)),X3))
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2916]) ).

cnf(c_0_2917_0,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X1)),X3))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2917]) ).

cnf(c_0_2917_1,axiom,
    ( ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X1)),X3))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2917]) ).

cnf(c_0_2917_2,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X1)),X3))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2917]) ).

cnf(c_0_2917_3,axiom,
    ( ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X1)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X1)),X3))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2917]) ).

cnf(c_0_2917_4,axiom,
    ( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X1)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X1)),X3))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2917]) ).

cnf(c_0_2917_5,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X1)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X1)),X3))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2917]) ).

cnf(c_0_2917_6,axiom,
    ( ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X1)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X1)),X3))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2917]) ).

cnf(c_0_2918_0,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_2918]) ).

cnf(c_0_2918_1,axiom,
    ( ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_2918]) ).

cnf(c_0_2918_2,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3))
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_2918]) ).

cnf(c_0_2918_3,axiom,
    ( ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X1)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3))
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_2918]) ).

cnf(c_0_2918_4,axiom,
    ( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X1)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3))
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_2918]) ).

cnf(c_0_2918_5,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X1)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3))
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2918]) ).

cnf(c_0_2919_0,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3))
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_2919]) ).

cnf(c_0_2919_1,axiom,
    ( ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3))
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_2919]) ).

cnf(c_0_2919_2,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_2919]) ).

cnf(c_0_2919_3,axiom,
    ( ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_2919]) ).

cnf(c_0_2919_4,axiom,
    ( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_2919]) ).

cnf(c_0_2919_5,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2919]) ).

cnf(c_0_2920_0,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2920]) ).

cnf(c_0_2920_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2920]) ).

cnf(c_0_2920_2,axiom,
    ( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2920]) ).

cnf(c_0_2920_3,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2920]) ).

cnf(c_0_2920_4,axiom,
    ( ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2920]) ).

cnf(c_0_2921_0,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2921]) ).

cnf(c_0_2921_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2921]) ).

cnf(c_0_2921_2,axiom,
    ( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2921]) ).

cnf(c_0_2921_3,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2921]) ).

cnf(c_0_2921_4,axiom,
    ( ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2921]) ).

cnf(c_0_2922_0,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2922]) ).

cnf(c_0_2922_1,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2922]) ).

cnf(c_0_2922_2,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2922]) ).

cnf(c_0_2922_3,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba)) ),
    inference(literals_permutation,[status(thm)],[c_0_2922]) ).

cnf(c_0_2923_0,axiom,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2923]) ).

cnf(c_0_2923_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2923]) ).

cnf(c_0_2923_2,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2923]) ).

cnf(c_0_2923_3,axiom,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2923]) ).

cnf(c_0_2923_4,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n ),
    inference(literals_permutation,[status(thm)],[c_0_2923]) ).

cnf(c_0_2924_0,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2924]) ).

cnf(c_0_2924_1,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2924]) ).

cnf(c_0_2924_2,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2924]) ).

cnf(c_0_2924_3,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab)) ),
    inference(literals_permutation,[status(thm)],[c_0_2924]) ).

cnf(c_0_2925_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(literals_permutation,[status(thm)],[c_0_2925]) ).

cnf(c_0_2925_1,axiom,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(literals_permutation,[status(thm)],[c_0_2925]) ).

cnf(c_0_2925_2,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(literals_permutation,[status(thm)],[c_0_2925]) ).

cnf(c_0_2925_3,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(literals_permutation,[status(thm)],[c_0_2925]) ).

cnf(c_0_2925_4,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2925]) ).

cnf(c_0_2926_0,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2926]) ).

cnf(c_0_2926_1,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2926]) ).

cnf(c_0_2926_2,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2926]) ).

cnf(c_0_2926_3,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(literals_permutation,[status(thm)],[c_0_2926]) ).

cnf(c_0_2927_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2927]) ).

cnf(c_0_2927_1,axiom,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2927]) ).

cnf(c_0_2927_2,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2927]) ).

cnf(c_0_2927_3,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2927]) ).

cnf(c_0_2927_4,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2927]) ).

cnf(c_0_2928_0,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2928]) ).

cnf(c_0_2928_1,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2928]) ).

cnf(c_0_2928_2,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2928]) ).

cnf(c_0_2928_3,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba)) ),
    inference(literals_permutation,[status(thm)],[c_0_2928]) ).

cnf(c_0_2929_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2929]) ).

cnf(c_0_2929_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2929]) ).

cnf(c_0_2929_2,axiom,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2929]) ).

cnf(c_0_2929_3,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2929]) ).

cnf(c_0_2929_4,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2929]) ).

cnf(c_0_2930_0,axiom,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),X2,hAPP(fun(X3,bool),X1,X4,X5)),hAPP(fun(X3,bool),X1,X4,X6)) = hAPP(fun(X3,bool),X1,X4,X6)
    | ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X5),X6))
    | ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X6))
    | ~ hBOOL(hAPP(fun(fun(X3,bool),X1),bool,hAPP(fun(X3,X1),fun(fun(fun(X3,bool),X1),bool),hAPP(X1,fun(fun(X3,X1),fun(fun(fun(X3,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X3,X1),fun(fun(fun(X3,bool),X1),bool))),finite908156982e_idem(X1,X3),X2),X7),X8),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_2930]) ).

cnf(c_0_2930_1,axiom,
    ( ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X5),X6))
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),X2,hAPP(fun(X3,bool),X1,X4,X5)),hAPP(fun(X3,bool),X1,X4,X6)) = hAPP(fun(X3,bool),X1,X4,X6)
    | ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X6))
    | ~ hBOOL(hAPP(fun(fun(X3,bool),X1),bool,hAPP(fun(X3,X1),fun(fun(fun(X3,bool),X1),bool),hAPP(X1,fun(fun(X3,X1),fun(fun(fun(X3,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X3,X1),fun(fun(fun(X3,bool),X1),bool))),finite908156982e_idem(X1,X3),X2),X7),X8),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_2930]) ).

cnf(c_0_2930_2,axiom,
    ( ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X6))
    | ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X5),X6))
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),X2,hAPP(fun(X3,bool),X1,X4,X5)),hAPP(fun(X3,bool),X1,X4,X6)) = hAPP(fun(X3,bool),X1,X4,X6)
    | ~ hBOOL(hAPP(fun(fun(X3,bool),X1),bool,hAPP(fun(X3,X1),fun(fun(fun(X3,bool),X1),bool),hAPP(X1,fun(fun(X3,X1),fun(fun(fun(X3,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X3,X1),fun(fun(fun(X3,bool),X1),bool))),finite908156982e_idem(X1,X3),X2),X7),X8),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_2930]) ).

cnf(c_0_2930_3,axiom,
    ( ~ hBOOL(hAPP(fun(fun(X3,bool),X1),bool,hAPP(fun(X3,X1),fun(fun(fun(X3,bool),X1),bool),hAPP(X1,fun(fun(X3,X1),fun(fun(fun(X3,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X3,X1),fun(fun(fun(X3,bool),X1),bool))),finite908156982e_idem(X1,X3),X2),X7),X8),X4))
    | ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X6))
    | ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X5),X6))
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),X2,hAPP(fun(X3,bool),X1,X4,X5)),hAPP(fun(X3,bool),X1,X4,X6)) = hAPP(fun(X3,bool),X1,X4,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_2930]) ).

cnf(c_0_2931_0,axiom,
    ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X3),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X4),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),X5))))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X3,sk1_esk65_5(X2,X1,X3,X5,X4))),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_2931]) ).

cnf(c_0_2931_1,axiom,
    ( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),hAPP(X1,X2,X3,sk1_esk65_5(X2,X1,X3,X5,X4))),X5))
    | hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X3),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X4),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),X5)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2931]) ).

cnf(c_0_2932_0,axiom,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),X2,hAPP(X3,X1,X4,X5)),hAPP(fun(X3,bool),X1,X6,X7)) = hAPP(fun(X3,bool),X1,X6,X7)
    | ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X5),X7))
    | ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X7))
    | ~ hBOOL(hAPP(fun(fun(X3,bool),X1),bool,hAPP(fun(X3,X1),fun(fun(fun(X3,bool),X1),bool),hAPP(X1,fun(fun(X3,X1),fun(fun(fun(X3,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X3,X1),fun(fun(fun(X3,bool),X1),bool))),finite908156982e_idem(X1,X3),X2),X8),X4),X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_2932]) ).

cnf(c_0_2932_1,axiom,
    ( ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X5),X7))
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),X2,hAPP(X3,X1,X4,X5)),hAPP(fun(X3,bool),X1,X6,X7)) = hAPP(fun(X3,bool),X1,X6,X7)
    | ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X7))
    | ~ hBOOL(hAPP(fun(fun(X3,bool),X1),bool,hAPP(fun(X3,X1),fun(fun(fun(X3,bool),X1),bool),hAPP(X1,fun(fun(X3,X1),fun(fun(fun(X3,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X3,X1),fun(fun(fun(X3,bool),X1),bool))),finite908156982e_idem(X1,X3),X2),X8),X4),X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_2932]) ).

cnf(c_0_2932_2,axiom,
    ( ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X7))
    | ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X5),X7))
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),X2,hAPP(X3,X1,X4,X5)),hAPP(fun(X3,bool),X1,X6,X7)) = hAPP(fun(X3,bool),X1,X6,X7)
    | ~ hBOOL(hAPP(fun(fun(X3,bool),X1),bool,hAPP(fun(X3,X1),fun(fun(fun(X3,bool),X1),bool),hAPP(X1,fun(fun(X3,X1),fun(fun(fun(X3,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X3,X1),fun(fun(fun(X3,bool),X1),bool))),finite908156982e_idem(X1,X3),X2),X8),X4),X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_2932]) ).

cnf(c_0_2932_3,axiom,
    ( ~ hBOOL(hAPP(fun(fun(X3,bool),X1),bool,hAPP(fun(X3,X1),fun(fun(fun(X3,bool),X1),bool),hAPP(X1,fun(fun(X3,X1),fun(fun(fun(X3,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X3,X1),fun(fun(fun(X3,bool),X1),bool))),finite908156982e_idem(X1,X3),X2),X8),X4),X6))
    | ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X7))
    | ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X5),X7))
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),X2,hAPP(X3,X1,X4,X5)),hAPP(fun(X3,bool),X1,X6,X7)) = hAPP(fun(X3,bool),X1,X6,X7) ),
    inference(literals_permutation,[status(thm)],[c_0_2932]) ).

cnf(c_0_2933_0,axiom,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2933]) ).

cnf(c_0_2933_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2933]) ).

cnf(c_0_2933_2,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2933]) ).

cnf(c_0_2933_3,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2933]) ).

cnf(c_0_2933_4,axiom,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n ),
    inference(literals_permutation,[status(thm)],[c_0_2933]) ).

cnf(c_0_2934_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(literals_permutation,[status(thm)],[c_0_2934]) ).

cnf(c_0_2934_1,axiom,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(literals_permutation,[status(thm)],[c_0_2934]) ).

cnf(c_0_2934_2,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(literals_permutation,[status(thm)],[c_0_2934]) ).

cnf(c_0_2934_3,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(literals_permutation,[status(thm)],[c_0_2934]) ).

cnf(c_0_2934_4,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2934]) ).

cnf(c_0_2935_0,axiom,
    ( hAPP(fun(X1,bool),nat,finite_card(X1),X2) = hAPP(fun(X3,bool),nat,finite_card(X3),X4)
    | ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X5),X4))
    | ~ hBOOL(hAPP(fun(fun(X3,X1),bool),bool,hAPP(fun(X3,X1),fun(fun(fun(X3,X1),bool),bool),member(fun(X3,X1)),X5),hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool)),pi(X3,X1),X4),hAPP(fun(X1,bool),fun(X3,fun(X1,bool)),combk(fun(X1,bool),X3),X2))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X6),X2))
    | ~ hBOOL(hAPP(fun(fun(X1,X3),bool),bool,hAPP(fun(X1,X3),fun(fun(fun(X1,X3),bool),bool),member(fun(X1,X3)),X6),hAPP(fun(X1,fun(X3,bool)),fun(fun(X1,X3),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X3,bool)),fun(fun(X1,X3),bool)),pi(X1,X3),X2),hAPP(fun(X3,bool),fun(X1,fun(X3,bool)),combk(fun(X3,bool),X1),X4)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2935]) ).

cnf(c_0_2935_1,axiom,
    ( ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X4))
    | hAPP(fun(X1,bool),nat,finite_card(X1),X2) = hAPP(fun(X3,bool),nat,finite_card(X3),X4)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X5),X4))
    | ~ hBOOL(hAPP(fun(fun(X3,X1),bool),bool,hAPP(fun(X3,X1),fun(fun(fun(X3,X1),bool),bool),member(fun(X3,X1)),X5),hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool)),pi(X3,X1),X4),hAPP(fun(X1,bool),fun(X3,fun(X1,bool)),combk(fun(X1,bool),X3),X2))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X6),X2))
    | ~ hBOOL(hAPP(fun(fun(X1,X3),bool),bool,hAPP(fun(X1,X3),fun(fun(fun(X1,X3),bool),bool),member(fun(X1,X3)),X6),hAPP(fun(X1,fun(X3,bool)),fun(fun(X1,X3),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X3,bool)),fun(fun(X1,X3),bool)),pi(X1,X3),X2),hAPP(fun(X3,bool),fun(X1,fun(X3,bool)),combk(fun(X3,bool),X1),X4)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2935]) ).

cnf(c_0_2935_2,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X4))
    | hAPP(fun(X1,bool),nat,finite_card(X1),X2) = hAPP(fun(X3,bool),nat,finite_card(X3),X4)
    | ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X5),X4))
    | ~ hBOOL(hAPP(fun(fun(X3,X1),bool),bool,hAPP(fun(X3,X1),fun(fun(fun(X3,X1),bool),bool),member(fun(X3,X1)),X5),hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool)),pi(X3,X1),X4),hAPP(fun(X1,bool),fun(X3,fun(X1,bool)),combk(fun(X1,bool),X3),X2))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X6),X2))
    | ~ hBOOL(hAPP(fun(fun(X1,X3),bool),bool,hAPP(fun(X1,X3),fun(fun(fun(X1,X3),bool),bool),member(fun(X1,X3)),X6),hAPP(fun(X1,fun(X3,bool)),fun(fun(X1,X3),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X3,bool)),fun(fun(X1,X3),bool)),pi(X1,X3),X2),hAPP(fun(X3,bool),fun(X1,fun(X3,bool)),combk(fun(X3,bool),X1),X4)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2935]) ).

cnf(c_0_2935_3,axiom,
    ( ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X5),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X4))
    | hAPP(fun(X1,bool),nat,finite_card(X1),X2) = hAPP(fun(X3,bool),nat,finite_card(X3),X4)
    | ~ hBOOL(hAPP(fun(fun(X3,X1),bool),bool,hAPP(fun(X3,X1),fun(fun(fun(X3,X1),bool),bool),member(fun(X3,X1)),X5),hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool)),pi(X3,X1),X4),hAPP(fun(X1,bool),fun(X3,fun(X1,bool)),combk(fun(X1,bool),X3),X2))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X6),X2))
    | ~ hBOOL(hAPP(fun(fun(X1,X3),bool),bool,hAPP(fun(X1,X3),fun(fun(fun(X1,X3),bool),bool),member(fun(X1,X3)),X6),hAPP(fun(X1,fun(X3,bool)),fun(fun(X1,X3),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X3,bool)),fun(fun(X1,X3),bool)),pi(X1,X3),X2),hAPP(fun(X3,bool),fun(X1,fun(X3,bool)),combk(fun(X3,bool),X1),X4)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2935]) ).

cnf(c_0_2935_4,axiom,
    ( ~ hBOOL(hAPP(fun(fun(X3,X1),bool),bool,hAPP(fun(X3,X1),fun(fun(fun(X3,X1),bool),bool),member(fun(X3,X1)),X5),hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool)),pi(X3,X1),X4),hAPP(fun(X1,bool),fun(X3,fun(X1,bool)),combk(fun(X1,bool),X3),X2))))
    | ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X5),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X4))
    | hAPP(fun(X1,bool),nat,finite_card(X1),X2) = hAPP(fun(X3,bool),nat,finite_card(X3),X4)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X6),X2))
    | ~ hBOOL(hAPP(fun(fun(X1,X3),bool),bool,hAPP(fun(X1,X3),fun(fun(fun(X1,X3),bool),bool),member(fun(X1,X3)),X6),hAPP(fun(X1,fun(X3,bool)),fun(fun(X1,X3),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X3,bool)),fun(fun(X1,X3),bool)),pi(X1,X3),X2),hAPP(fun(X3,bool),fun(X1,fun(X3,bool)),combk(fun(X3,bool),X1),X4)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2935]) ).

cnf(c_0_2935_5,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X6),X2))
    | ~ hBOOL(hAPP(fun(fun(X3,X1),bool),bool,hAPP(fun(X3,X1),fun(fun(fun(X3,X1),bool),bool),member(fun(X3,X1)),X5),hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool)),pi(X3,X1),X4),hAPP(fun(X1,bool),fun(X3,fun(X1,bool)),combk(fun(X1,bool),X3),X2))))
    | ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X5),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X4))
    | hAPP(fun(X1,bool),nat,finite_card(X1),X2) = hAPP(fun(X3,bool),nat,finite_card(X3),X4)
    | ~ hBOOL(hAPP(fun(fun(X1,X3),bool),bool,hAPP(fun(X1,X3),fun(fun(fun(X1,X3),bool),bool),member(fun(X1,X3)),X6),hAPP(fun(X1,fun(X3,bool)),fun(fun(X1,X3),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X3,bool)),fun(fun(X1,X3),bool)),pi(X1,X3),X2),hAPP(fun(X3,bool),fun(X1,fun(X3,bool)),combk(fun(X3,bool),X1),X4)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2935]) ).

cnf(c_0_2935_6,axiom,
    ( ~ hBOOL(hAPP(fun(fun(X1,X3),bool),bool,hAPP(fun(X1,X3),fun(fun(fun(X1,X3),bool),bool),member(fun(X1,X3)),X6),hAPP(fun(X1,fun(X3,bool)),fun(fun(X1,X3),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X3,bool)),fun(fun(X1,X3),bool)),pi(X1,X3),X2),hAPP(fun(X3,bool),fun(X1,fun(X3,bool)),combk(fun(X3,bool),X1),X4))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X6),X2))
    | ~ hBOOL(hAPP(fun(fun(X3,X1),bool),bool,hAPP(fun(X3,X1),fun(fun(fun(X3,X1),bool),bool),member(fun(X3,X1)),X5),hAPP(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X3,fun(X1,bool)),fun(fun(X3,X1),bool)),pi(X3,X1),X4),hAPP(fun(X1,bool),fun(X3,fun(X1,bool)),combk(fun(X1,bool),X3),X2))))
    | ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,X1),fun(fun(X3,bool),bool),inj_on(X3,X1),X5),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X4))
    | hAPP(fun(X1,bool),nat,finite_card(X1),X2) = hAPP(fun(X3,bool),nat,finite_card(X3),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2935]) ).

cnf(c_0_2936_0,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2936]) ).

cnf(c_0_2936_1,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2936]) ).

cnf(c_0_2936_2,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_2936]) ).

cnf(c_0_2937_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2937]) ).

cnf(c_0_2937_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2937]) ).

cnf(c_0_2937_2,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2937]) ).

cnf(c_0_2937_3,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2937]) ).

cnf(c_0_2938_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2938]) ).

cnf(c_0_2938_1,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2938]) ).

cnf(c_0_2938_2,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2938]) ).

cnf(c_0_2938_3,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2938]) ).

cnf(c_0_2938_4,axiom,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),c),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2938]) ).

cnf(c_0_2939_0,axiom,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2939]) ).

cnf(c_0_2939_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2939]) ).

cnf(c_0_2939_2,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2939]) ).

cnf(c_0_2939_3,axiom,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2939]) ).

cnf(c_0_2939_4,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n ),
    inference(literals_permutation,[status(thm)],[c_0_2939]) ).

cnf(c_0_2940_0,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2940]) ).

cnf(c_0_2940_1,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2940]) ).

cnf(c_0_2940_2,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2940]) ).

cnf(c_0_2940_3,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(literals_permutation,[status(thm)],[c_0_2940]) ).

cnf(c_0_2941_0,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2941]) ).

cnf(c_0_2941_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2941]) ).

cnf(c_0_2941_2,axiom,
    ( ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2941]) ).

cnf(c_0_2941_3,axiom,
    ( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2941]) ).

cnf(c_0_2941_4,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2941]) ).

cnf(c_0_2941_5,axiom,
    ( ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2941]) ).

cnf(c_0_2941_6,axiom,
    ( ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2941]) ).

cnf(c_0_2942_0,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2942]) ).

cnf(c_0_2942_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2942]) ).

cnf(c_0_2942_2,axiom,
    ( ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2942]) ).

cnf(c_0_2942_3,axiom,
    ( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2942]) ).

cnf(c_0_2942_4,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2942]) ).

cnf(c_0_2942_5,axiom,
    ( ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2942]) ).

cnf(c_0_2942_6,axiom,
    ( ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2942]) ).

cnf(c_0_2943_0,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2943]) ).

cnf(c_0_2943_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2943]) ).

cnf(c_0_2943_2,axiom,
    ( ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2943]) ).

cnf(c_0_2943_3,axiom,
    ( ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2943]) ).

cnf(c_0_2943_4,axiom,
    ( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2943]) ).

cnf(c_0_2943_5,axiom,
    ( ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2943]) ).

cnf(c_0_2943_6,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2943]) ).

cnf(c_0_2944_0,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X5)),X3))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2944]) ).

cnf(c_0_2944_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X5)),X3))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2944]) ).

cnf(c_0_2944_2,axiom,
    ( ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X5)),X3))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2944]) ).

cnf(c_0_2944_3,axiom,
    ( ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X5)),X3))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2944]) ).

cnf(c_0_2944_4,axiom,
    ( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X5)),X3))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2944]) ).

cnf(c_0_2944_5,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X5)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2944]) ).

cnf(c_0_2944_6,axiom,
    ( ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X5)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2944]) ).

cnf(c_0_2945_0,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2945]) ).

cnf(c_0_2945_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2945]) ).

cnf(c_0_2945_2,axiom,
    ( ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2945]) ).

cnf(c_0_2945_3,axiom,
    ( ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2945]) ).

cnf(c_0_2945_4,axiom,
    ( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2945]) ).

cnf(c_0_2945_5,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2945]) ).

cnf(c_0_2945_6,axiom,
    ( ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2945]) ).

cnf(c_0_2946_0,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2946]) ).

cnf(c_0_2946_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2946]) ).

cnf(c_0_2946_2,axiom,
    ( ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2946]) ).

cnf(c_0_2946_3,axiom,
    ( ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2946]) ).

cnf(c_0_2946_4,axiom,
    ( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2946]) ).

cnf(c_0_2946_5,axiom,
    ( ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2946]) ).

cnf(c_0_2946_6,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2946]) ).

cnf(c_0_2947_0,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X1)),X3))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2947]) ).

cnf(c_0_2947_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X1)),X3))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2947]) ).

cnf(c_0_2947_2,axiom,
    ( ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X1)),X3))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2947]) ).

cnf(c_0_2947_3,axiom,
    ( ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X1)),X3))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2947]) ).

cnf(c_0_2947_4,axiom,
    ( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X1)),X3))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2947]) ).

cnf(c_0_2947_5,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X1)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2947]) ).

cnf(c_0_2947_6,axiom,
    ( ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X1)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2947]) ).

cnf(c_0_2948_0,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2948]) ).

cnf(c_0_2948_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2948]) ).

cnf(c_0_2948_2,axiom,
    ( ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2948]) ).

cnf(c_0_2948_3,axiom,
    ( ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2948]) ).

cnf(c_0_2948_4,axiom,
    ( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2948]) ).

cnf(c_0_2948_5,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2948]) ).

cnf(c_0_2948_6,axiom,
    ( ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2948]) ).

cnf(c_0_2949_0,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2949]) ).

cnf(c_0_2949_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2949]) ).

cnf(c_0_2949_2,axiom,
    ( ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2949]) ).

cnf(c_0_2949_3,axiom,
    ( ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2949]) ).

cnf(c_0_2949_4,axiom,
    ( ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2949]) ).

cnf(c_0_2949_5,axiom,
    ( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2949]) ).

cnf(c_0_2949_6,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2949]) ).

cnf(c_0_2950_0,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2950]) ).

cnf(c_0_2950_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2950]) ).

cnf(c_0_2950_2,axiom,
    ( ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2950]) ).

cnf(c_0_2950_3,axiom,
    ( ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2950]) ).

cnf(c_0_2950_4,axiom,
    ( ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2950]) ).

cnf(c_0_2950_5,axiom,
    ( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2950]) ).

cnf(c_0_2950_6,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2950]) ).

cnf(c_0_2951_0,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2951]) ).

cnf(c_0_2951_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2951]) ).

cnf(c_0_2951_2,axiom,
    ( ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2951]) ).

cnf(c_0_2951_3,axiom,
    ( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2951]) ).

cnf(c_0_2951_4,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2951]) ).

cnf(c_0_2951_5,axiom,
    ( ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X2)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2951]) ).

cnf(c_0_2952_0,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2952]) ).

cnf(c_0_2952_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2952]) ).

cnf(c_0_2952_2,axiom,
    ( ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2952]) ).

cnf(c_0_2952_3,axiom,
    ( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2952]) ).

cnf(c_0_2952_4,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2952]) ).

cnf(c_0_2952_5,axiom,
    ( ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X5)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2952]) ).

cnf(c_0_2953_0,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(literals_permutation,[status(thm)],[c_0_2953]) ).

cnf(c_0_2953_1,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(literals_permutation,[status(thm)],[c_0_2953]) ).

cnf(c_0_2953_2,axiom,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(literals_permutation,[status(thm)],[c_0_2953]) ).

cnf(c_0_2953_3,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_2953]) ).

cnf(c_0_2954_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba)) ),
    inference(literals_permutation,[status(thm)],[c_0_2954]) ).

cnf(c_0_2954_1,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba)) ),
    inference(literals_permutation,[status(thm)],[c_0_2954]) ).

cnf(c_0_2954_2,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba)) ),
    inference(literals_permutation,[status(thm)],[c_0_2954]) ).

cnf(c_0_2954_3,axiom,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba)) ),
    inference(literals_permutation,[status(thm)],[c_0_2954]) ).

cnf(c_0_2954_4,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2954]) ).

cnf(c_0_2955_0,axiom,
    ( ti(fun(product_prod(X1,X2),bool),X3) = ti(fun(product_prod(X1,X2),bool),X4)
    | hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),member(product_prod(X1,X2)),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),sk1_esk21_4(X1,X2,X4,X3)),sk1_esk22_4(X1,X2,X4,X3))),X4))
    | hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),member(product_prod(X1,X2)),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),sk1_esk21_4(X1,X2,X4,X3)),sk1_esk22_4(X1,X2,X4,X3))),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2955]) ).

cnf(c_0_2955_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),member(product_prod(X1,X2)),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),sk1_esk21_4(X1,X2,X4,X3)),sk1_esk22_4(X1,X2,X4,X3))),X4))
    | ti(fun(product_prod(X1,X2),bool),X3) = ti(fun(product_prod(X1,X2),bool),X4)
    | hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),member(product_prod(X1,X2)),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),sk1_esk21_4(X1,X2,X4,X3)),sk1_esk22_4(X1,X2,X4,X3))),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2955]) ).

cnf(c_0_2955_2,axiom,
    ( hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),member(product_prod(X1,X2)),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),sk1_esk21_4(X1,X2,X4,X3)),sk1_esk22_4(X1,X2,X4,X3))),X3))
    | hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),member(product_prod(X1,X2)),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),sk1_esk21_4(X1,X2,X4,X3)),sk1_esk22_4(X1,X2,X4,X3))),X4))
    | ti(fun(product_prod(X1,X2),bool),X3) = ti(fun(product_prod(X1,X2),bool),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_2955]) ).

cnf(c_0_2956_0,axiom,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2956]) ).

cnf(c_0_2956_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2956]) ).

cnf(c_0_2956_2,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2956]) ).

cnf(c_0_2956_3,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2956]) ).

cnf(c_0_2956_4,axiom,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n ),
    inference(literals_permutation,[status(thm)],[c_0_2956]) ).

cnf(c_0_2957_0,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,X4)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk14_4(X3,X4,X1,X2))))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2957]) ).

cnf(c_0_2957_1,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk14_4(X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,X4)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2957]) ).

cnf(c_0_2957_2,axiom,
    ( ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk14_4(X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,X4)))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2957]) ).

cnf(c_0_2957_3,axiom,
    ( ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,X3))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X4),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X4,sk1_esk14_4(X3,X4,X1,X2))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X3,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_2957]) ).

cnf(c_0_2958_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2958]) ).

cnf(c_0_2958_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2958]) ).

cnf(c_0_2958_2,axiom,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2958]) ).

cnf(c_0_2958_3,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2958]) ).

cnf(c_0_2958_4,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2958]) ).

cnf(c_0_2959_0,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X5) ),
    inference(literals_permutation,[status(thm)],[c_0_2959]) ).

cnf(c_0_2959_1,axiom,
    ( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X5) ),
    inference(literals_permutation,[status(thm)],[c_0_2959]) ).

cnf(c_0_2959_2,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X5) ),
    inference(literals_permutation,[status(thm)],[c_0_2959]) ).

cnf(c_0_2959_3,axiom,
    ( ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X5)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2959]) ).

cnf(c_0_2960_0,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X5) ),
    inference(literals_permutation,[status(thm)],[c_0_2960]) ).

cnf(c_0_2960_1,axiom,
    ( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X5) ),
    inference(literals_permutation,[status(thm)],[c_0_2960]) ).

cnf(c_0_2960_2,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X5) ),
    inference(literals_permutation,[status(thm)],[c_0_2960]) ).

cnf(c_0_2960_3,axiom,
    ( ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X5)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2960]) ).

cnf(c_0_2961_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2961]) ).

cnf(c_0_2961_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2961]) ).

cnf(c_0_2961_2,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2961]) ).

cnf(c_0_2961_3,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2961]) ).

cnf(c_0_2962_0,axiom,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),X2,X3),X3) = ti(X1,X3)
    | ~ hBOOL(hAPP(fun(fun(X4,bool),X1),bool,hAPP(fun(X4,X1),fun(fun(fun(X4,bool),X1),bool),hAPP(X1,fun(fun(X4,X1),fun(fun(fun(X4,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X4,X1),fun(fun(fun(X4,bool),X1),bool))),finite908156982e_idem(X1,X4),X2),X5),X6),X7)) ),
    inference(literals_permutation,[status(thm)],[c_0_2962]) ).

cnf(c_0_2962_1,axiom,
    ( ~ hBOOL(hAPP(fun(fun(X4,bool),X1),bool,hAPP(fun(X4,X1),fun(fun(fun(X4,bool),X1),bool),hAPP(X1,fun(fun(X4,X1),fun(fun(fun(X4,bool),X1),bool)),hAPP(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X4,X1),fun(fun(fun(X4,bool),X1),bool))),finite908156982e_idem(X1,X4),X2),X5),X6),X7))
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),X2,X3),X3) = ti(X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2962]) ).

cnf(c_0_2963_0,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2963]) ).

cnf(c_0_2963_1,axiom,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2963]) ).

cnf(c_0_2963_2,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_2963]) ).

cnf(c_0_2963_3,axiom,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_2963]) ).

cnf(c_0_2964_0,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2964]) ).

cnf(c_0_2964_1,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2964]) ).

cnf(c_0_2964_2,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e))) ),
    inference(literals_permutation,[status(thm)],[c_0_2964]) ).

cnf(c_0_2965_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba)) ),
    inference(literals_permutation,[status(thm)],[c_0_2965]) ).

cnf(c_0_2965_1,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba)) ),
    inference(literals_permutation,[status(thm)],[c_0_2965]) ).

cnf(c_0_2965_2,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba)) ),
    inference(literals_permutation,[status(thm)],[c_0_2965]) ).

cnf(c_0_2965_3,axiom,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba)) ),
    inference(literals_permutation,[status(thm)],[c_0_2965]) ).

cnf(c_0_2965_4,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2965]) ).

cnf(c_0_2966_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2966]) ).

cnf(c_0_2966_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2966]) ).

cnf(c_0_2966_2,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2966]) ).

cnf(c_0_2966_3,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2966]) ).

cnf(c_0_2967_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_2967]) ).

cnf(c_0_2967_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_2967]) ).

cnf(c_0_2967_2,axiom,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_2967]) ).

cnf(c_0_2967_3,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2967]) ).

cnf(c_0_2968_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2968]) ).

cnf(c_0_2968_1,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2968]) ).

cnf(c_0_2968_2,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2968]) ).

cnf(c_0_2968_3,axiom,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2968]) ).

cnf(c_0_2968_4,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2968]) ).

cnf(c_0_2969_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),one_one(X1)),X2)),X2)),zero_zero(X1)))
    | ~ linordered_idom(X1)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),ring_1_Ints(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_2969]) ).

cnf(c_0_2969_1,axiom,
    ( ~ linordered_idom(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),one_one(X1)),X2)),X2)),zero_zero(X1)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),ring_1_Ints(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_2969]) ).

cnf(c_0_2969_2,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),ring_1_Ints(X1)))
    | ~ linordered_idom(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),one_one(X1)),X2)),X2)),zero_zero(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_2969]) ).

cnf(c_0_2969_3,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),ring_1_Ints(X1)))
    | ~ linordered_idom(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),one_one(X1)),X2)),X2)),zero_zero(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_2969]) ).

cnf(c_0_2970_0,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X2,bool),nat,finite_card(X2),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X4))),hAPP(fun(X1,bool),nat,finite_card(X1),X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_2970]) ).

cnf(c_0_2970_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X2,bool),nat,finite_card(X2),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X4))),hAPP(fun(X1,bool),nat,finite_card(X1),X4)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_2970]) ).

cnf(c_0_2971_0,axiom,
    ( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X1),X2),X3)),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X1),arrow_2064824852le_Lin)) ),
    inference(literals_permutation,[status(thm)],[c_0_2971]) ).

cnf(c_0_2971_1,axiom,
    ( ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X1),X2),X3)),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X1),arrow_2064824852le_Lin)) ),
    inference(literals_permutation,[status(thm)],[c_0_2971]) ).

cnf(c_0_2971_2,axiom,
    ( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X1),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X1),X2),X3)),arrow_2064824852le_Lin)) ),
    inference(literals_permutation,[status(thm)],[c_0_2971]) ).

cnf(c_0_2972_0,axiom,
    ( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X1),X2),X3)),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X1),arrow_2064824852le_Lin)) ),
    inference(literals_permutation,[status(thm)],[c_0_2972]) ).

cnf(c_0_2972_1,axiom,
    ( ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X1),X2),X3)),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X1),arrow_2064824852le_Lin)) ),
    inference(literals_permutation,[status(thm)],[c_0_2972]) ).

cnf(c_0_2972_2,axiom,
    ( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X1),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X1),X2),X3)),arrow_2064824852le_Lin)) ),
    inference(literals_permutation,[status(thm)],[c_0_2972]) ).

cnf(c_0_2973_0,axiom,
    ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sk1_esk12_1(X1)),sk1_esk13_1(X1))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,sk1_esk11_1(X1))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sk1_esk12_1(X1)),sk1_esk13_1(X1))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,sk1_esk10_1(X1)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2973]) ).

cnf(c_0_2973_1,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sk1_esk12_1(X1)),sk1_esk13_1(X1))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,sk1_esk11_1(X1))))
    | hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sk1_esk12_1(X1)),sk1_esk13_1(X1))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,sk1_esk10_1(X1)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2973]) ).

cnf(c_0_2973_2,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sk1_esk12_1(X1)),sk1_esk13_1(X1))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,sk1_esk10_1(X1))))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sk1_esk12_1(X1)),sk1_esk13_1(X1))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,sk1_esk11_1(X1))))
    | hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_2973]) ).

cnf(c_0_2974_0,axiom,
    ( ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X1),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),X1))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X2)),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_2974]) ).

cnf(c_0_2974_1,axiom,
    ( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X1),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),X1))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X2)),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_2974]) ).

cnf(c_0_2974_2,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),X1))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X1),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X2)),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_2974]) ).

cnf(c_0_2974_3,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X2)),X1))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),X1))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X1),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_2974]) ).

cnf(c_0_2975_0,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin)) ),
    inference(literals_permutation,[status(thm)],[c_0_2975]) ).

cnf(c_0_2975_1,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin)) ),
    inference(literals_permutation,[status(thm)],[c_0_2975]) ).

cnf(c_0_2975_2,axiom,
    ( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X1)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2975]) ).

cnf(c_0_2976_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(X1,bool)),combc(X1,fun(X1,bool),bool),member(X1)),X2)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(X1,bool)),combc(X1,fun(X1,bool),bool),member(X1)),X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_2976]) ).

cnf(c_0_2976_1,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(X1,bool)),combc(X1,fun(X1,bool),bool),member(X1)),X2)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(X1,bool)),combc(X1,fun(X1,bool),bool),member(X1)),X3)))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2976]) ).

cnf(c_0_2977_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),hAPP(fun(X2,X3),fun(X2,X1),hAPP(fun(X3,X1),fun(fun(X2,X3),fun(X2,X1)),combb(X3,X1,X2),X4),X5)),top_top(fun(X2,bool)))))
    | ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),hAPP(fun(X2,bool),fun(X3,bool),hAPP(fun(X2,X3),fun(fun(X2,bool),fun(X3,bool)),image(X2,X3),X5),top_top(fun(X2,bool))))) ),
    inference(literals_permutation,[status(thm)],[c_0_2977]) ).

cnf(c_0_2977_1,axiom,
    ( ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),hAPP(fun(X2,bool),fun(X3,bool),hAPP(fun(X2,X3),fun(fun(X2,bool),fun(X3,bool)),image(X2,X3),X5),top_top(fun(X2,bool)))))
    | hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),hAPP(fun(X2,X3),fun(X2,X1),hAPP(fun(X3,X1),fun(fun(X2,X3),fun(X2,X1)),combb(X3,X1,X2),X4),X5)),top_top(fun(X2,bool))))) ),
    inference(literals_permutation,[status(thm)],[c_0_2977]) ).

cnf(c_0_2978_0,axiom,
    ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(fun(X1,X2),bool),fun(fun(fun(X1,X2),bool),bool),ord_less_eq(fun(fun(X1,X2),bool)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X3),X4)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X3),X5)))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk52_5(X2,X1,X4,X5,X3)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2978]) ).

cnf(c_0_2978_1,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk52_5(X2,X1,X4,X5,X3)),X3))
    | hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(fun(X1,X2),bool),fun(fun(fun(X1,X2),bool),bool),ord_less_eq(fun(fun(X1,X2),bool)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X3),X4)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X3),X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_2978]) ).

cnf(c_0_2979_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2979]) ).

cnf(c_0_2979_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2979]) ).

cnf(c_0_2979_2,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2979]) ).

cnf(c_0_2979_3,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2979]) ).

cnf(c_0_2980_0,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X4)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X3),X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_2980]) ).

cnf(c_0_2980_1,axiom,
    ( ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X4)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X3),X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_2980]) ).

cnf(c_0_2980_2,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X3),X4)))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X4)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2980]) ).

cnf(c_0_2981_0,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X3),X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_2981]) ).

cnf(c_0_2981_1,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X3),X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_2981]) ).

cnf(c_0_2981_2,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X3),X4)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2981]) ).

cnf(c_0_2982_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2982]) ).

cnf(c_0_2982_1,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2982]) ).

cnf(c_0_2982_2,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2982]) ).

cnf(c_0_2982_3,axiom,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2982]) ).

cnf(c_0_2982_4,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)),e)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_2982]) ).

cnf(c_0_2983_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X2,X1,hAPP(fun(X1,X2),fun(X2,X1),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)),hilbert_inv_into(X1,X2),X3),X4),X5)),X3))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X5),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X4),X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_2983]) ).

cnf(c_0_2983_1,axiom,
    ( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X5),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X4),X3)))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X2,X1,hAPP(fun(X1,X2),fun(X2,X1),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)),hilbert_inv_into(X1,X2),X3),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2983]) ).

cnf(c_0_2984_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,X1,X2)),X3)),hAPP(nat,nat,X1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,X1,sk1_esk61_3(X2,X3,X1))),hAPP(nat,nat,X1,sk1_esk62_3(X2,X3,X1)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2984]) ).

cnf(c_0_2984_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,X1,sk1_esk61_3(X2,X3,X1))),hAPP(nat,nat,X1,sk1_esk62_3(X2,X3,X1))))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,X1,X2)),X3)),hAPP(nat,nat,X1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2984]) ).

cnf(c_0_2986_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X4))
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,X2,sk1_esk91_4(X1,X3,X4,X2))),hAPP(nat,X1,X2,hAPP(nat,nat,suc,sk1_esk91_4(X1,X3,X4,X2)))))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,X2,X3)),hAPP(nat,X1,X2,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_2986]) ).

cnf(c_0_2986_1,axiom,
    ( ~ order(X1)
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,X2,sk1_esk91_4(X1,X3,X4,X2))),hAPP(nat,X1,X2,hAPP(nat,nat,suc,sk1_esk91_4(X1,X3,X4,X2)))))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,X2,X3)),hAPP(nat,X1,X2,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_2986]) ).

cnf(c_0_2986_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,X2,sk1_esk91_4(X1,X3,X4,X2))),hAPP(nat,X1,X2,hAPP(nat,nat,suc,sk1_esk91_4(X1,X3,X4,X2)))))
    | ~ order(X1)
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,X2,X3)),hAPP(nat,X1,X2,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_2986]) ).

cnf(c_0_2986_3,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,X2,X3)),hAPP(nat,X1,X2,X4)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,X2,sk1_esk91_4(X1,X3,X4,X2))),hAPP(nat,X1,X2,hAPP(nat,nat,suc,sk1_esk91_4(X1,X3,X4,X2)))))
    | ~ order(X1)
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_2986]) ).

cnf(c_0_2987_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X4)),X5))
    | ~ hBOOL(hAPP(fun(fun(X2,X1),bool),bool,hAPP(fun(X2,X1),fun(fun(fun(X2,X1),bool),bool),member(fun(X2,X1)),X3),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,X1),bool),hAPP(fun(X2,bool),fun(fun(X2,fun(X1,bool)),fun(fun(X2,X1),bool)),pi(X2,X1),X4),hAPP(fun(X1,bool),fun(X2,fun(X1,bool)),combk(fun(X1,bool),X2),X5)))) ),
    inference(literals_permutation,[status(thm)],[c_0_2987]) ).

cnf(c_0_2987_1,axiom,
    ( ~ hBOOL(hAPP(fun(fun(X2,X1),bool),bool,hAPP(fun(X2,X1),fun(fun(fun(X2,X1),bool),bool),member(fun(X2,X1)),X3),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,X1),bool),hAPP(fun(X2,bool),fun(fun(X2,fun(X1,bool)),fun(fun(X2,X1),bool)),pi(X2,X1),X4),hAPP(fun(X1,bool),fun(X2,fun(X1,bool)),combk(fun(X1,bool),X2),X5))))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X4)),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_2987]) ).

cnf(c_0_2988_0,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2988]) ).

cnf(c_0_2988_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2988]) ).

cnf(c_0_2988_2,axiom,
    ( ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2988]) ).

cnf(c_0_2988_3,axiom,
    ( ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2988]) ).

cnf(c_0_2988_4,axiom,
    ( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2988]) ).

cnf(c_0_2988_5,axiom,
    ( ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2988]) ).

cnf(c_0_2988_6,axiom,
    ( ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2988]) ).

cnf(c_0_2989_0,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2989]) ).

cnf(c_0_2989_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2989]) ).

cnf(c_0_2989_2,axiom,
    ( ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2989]) ).

cnf(c_0_2989_3,axiom,
    ( ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2989]) ).

cnf(c_0_2989_4,axiom,
    ( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2989]) ).

cnf(c_0_2989_5,axiom,
    ( ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2989]) ).

cnf(c_0_2989_6,axiom,
    ( ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2989]) ).

cnf(c_0_2990_0,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2990]) ).

cnf(c_0_2990_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2990]) ).

cnf(c_0_2990_2,axiom,
    ( ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2990]) ).

cnf(c_0_2990_3,axiom,
    ( ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2990]) ).

cnf(c_0_2990_4,axiom,
    ( ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2990]) ).

cnf(c_0_2990_5,axiom,
    ( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2990]) ).

cnf(c_0_2990_6,axiom,
    ( ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2990]) ).

cnf(c_0_2991_0,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2991]) ).

cnf(c_0_2991_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2991]) ).

cnf(c_0_2991_2,axiom,
    ( ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2991]) ).

cnf(c_0_2991_3,axiom,
    ( ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2991]) ).

cnf(c_0_2991_4,axiom,
    ( ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2991]) ).

cnf(c_0_2991_5,axiom,
    ( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2991]) ).

cnf(c_0_2991_6,axiom,
    ( ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2991]) ).

cnf(c_0_2992_0,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2992]) ).

cnf(c_0_2992_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2992]) ).

cnf(c_0_2992_2,axiom,
    ( ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2992]) ).

cnf(c_0_2992_3,axiom,
    ( ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2992]) ).

cnf(c_0_2992_4,axiom,
    ( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_2992]) ).

cnf(c_0_2992_5,axiom,
    ( ti(arrow_490897120le_alt,X5) != ti(arrow_490897120le_alt,X1)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X5) = ti(arrow_490897120le_alt,X1)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1322701812_below,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2992]) ).

cnf(c_0_2993_0,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2993]) ).

cnf(c_0_2993_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2993]) ).

cnf(c_0_2993_2,axiom,
    ( ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2993]) ).

cnf(c_0_2993_3,axiom,
    ( ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2993]) ).

cnf(c_0_2993_4,axiom,
    ( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2993]) ).

cnf(c_0_2993_5,axiom,
    ( ti(arrow_490897120le_alt,X4) != ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X3),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X4) = ti(arrow_490897120le_alt,X5)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X4),X5)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_14103264_above,X3),X1),X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_2993]) ).

cnf(c_0_2994_0,axiom,
    ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sk1_esk12_1(X1)),sk1_esk13_1(X1))),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),sk1_esk11_1(X1),X2)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sk1_esk12_1(X1)),sk1_esk13_1(X1))),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),sk1_esk10_1(X1),X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_2994]) ).

cnf(c_0_2994_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sk1_esk12_1(X1)),sk1_esk13_1(X1))),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),sk1_esk11_1(X1),X2)))
    | hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sk1_esk12_1(X1)),sk1_esk13_1(X1))),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),sk1_esk10_1(X1),X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_2994]) ).

cnf(c_0_2994_2,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sk1_esk12_1(X1)),sk1_esk13_1(X1))),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),sk1_esk10_1(X1),X2)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sk1_esk12_1(X1)),sk1_esk13_1(X1))),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),sk1_esk11_1(X1),X2)))
    | hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_2994]) ).

cnf(c_0_2995_0,axiom,
    ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sk1_esk12_1(X1)),sk1_esk13_1(X1))),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),sk1_esk10_1(X1),X2)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sk1_esk12_1(X1)),sk1_esk13_1(X1))),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),sk1_esk11_1(X1),X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_2995]) ).

cnf(c_0_2995_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sk1_esk12_1(X1)),sk1_esk13_1(X1))),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),sk1_esk10_1(X1),X2)))
    | hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sk1_esk12_1(X1)),sk1_esk13_1(X1))),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),sk1_esk11_1(X1),X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_2995]) ).

cnf(c_0_2995_2,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sk1_esk12_1(X1)),sk1_esk13_1(X1))),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),sk1_esk11_1(X1),X2)))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sk1_esk12_1(X1)),sk1_esk13_1(X1))),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),sk1_esk10_1(X1),X2)))
    | hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_2995]) ).

cnf(c_0_2996_0,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X3),X4)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X4)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2996]) ).

cnf(c_0_2996_1,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X3),X4)))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X4)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2996]) ).

cnf(c_0_2996_2,axiom,
    ( ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X3),X4)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2996]) ).

cnf(c_0_2996_3,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X3),X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_2996]) ).

cnf(c_0_2997_0,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X3),X4)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2997]) ).

cnf(c_0_2997_1,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X3),X4)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2997]) ).

cnf(c_0_2997_2,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X3),X4)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2997]) ).

cnf(c_0_2997_3,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X3),X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_2997]) ).

cnf(c_0_2998_0,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X3),X4)))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2998]) ).

cnf(c_0_2998_1,axiom,
    ( ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X4)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X3),X4)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2998]) ).

cnf(c_0_2998_2,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X4)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X3),X4)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2998]) ).

cnf(c_0_2998_3,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X4)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X3),X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_2998]) ).

cnf(c_0_2999_0,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X3),X4)))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2999]) ).

cnf(c_0_2999_1,axiom,
    ( ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X4)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X3),X4)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2999]) ).

cnf(c_0_2999_2,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X4)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X3),X4)))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_2999]) ).

cnf(c_0_2999_3,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),X3))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X4)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X3),X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_2999]) ).

cnf(c_0_3000_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X5))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),top_top(fun(X1,bool))))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X4)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_3000]) ).

cnf(c_0_3000_1,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),top_top(fun(X1,bool))))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X5))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X4)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_3000]) ).

cnf(c_0_3000_2,axiom,
    ( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X4)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X5)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),top_top(fun(X1,bool))))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_3000]) ).

cnf(c_0_3001_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,X2,X3)),hAPP(nat,X1,X2,X4)))
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,X2,sk1_esk91_4(X1,X3,X4,X2))),hAPP(nat,X1,X2,hAPP(nat,nat,suc,sk1_esk91_4(X1,X3,X4,X2)))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3001]) ).

cnf(c_0_3001_1,axiom,
    ( ~ order(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,X2,X3)),hAPP(nat,X1,X2,X4)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,X2,sk1_esk91_4(X1,X3,X4,X2))),hAPP(nat,X1,X2,hAPP(nat,nat,suc,sk1_esk91_4(X1,X3,X4,X2)))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3001]) ).

cnf(c_0_3001_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,X2,sk1_esk91_4(X1,X3,X4,X2))),hAPP(nat,X1,X2,hAPP(nat,nat,suc,sk1_esk91_4(X1,X3,X4,X2)))))
    | ~ order(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,X2,X3)),hAPP(nat,X1,X2,X4)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3001]) ).

cnf(c_0_3001_3,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,X2,sk1_esk91_4(X1,X3,X4,X2))),hAPP(nat,X1,X2,hAPP(nat,nat,suc,sk1_esk91_4(X1,X3,X4,X2)))))
    | ~ order(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,X2,X3)),hAPP(nat,X1,X2,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_3001]) ).

cnf(c_0_3002_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,X2,X3)),hAPP(nat,X1,X2,X4)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,X2,sk1_esk90_4(X1,X3,X4,X2))),hAPP(nat,X1,X2,hAPP(nat,nat,suc,sk1_esk90_4(X1,X3,X4,X2)))))
    | ~ order(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3002]) ).

cnf(c_0_3002_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X4))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,X2,X3)),hAPP(nat,X1,X2,X4)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,X2,sk1_esk90_4(X1,X3,X4,X2))),hAPP(nat,X1,X2,hAPP(nat,nat,suc,sk1_esk90_4(X1,X3,X4,X2)))))
    | ~ order(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3002]) ).

cnf(c_0_3002_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,X2,sk1_esk90_4(X1,X3,X4,X2))),hAPP(nat,X1,X2,hAPP(nat,nat,suc,sk1_esk90_4(X1,X3,X4,X2)))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X4))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,X2,X3)),hAPP(nat,X1,X2,X4)))
    | ~ order(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3002]) ).

cnf(c_0_3002_3,axiom,
    ( ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,X2,sk1_esk90_4(X1,X3,X4,X2))),hAPP(nat,X1,X2,hAPP(nat,nat,suc,sk1_esk90_4(X1,X3,X4,X2)))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X4))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(nat,X1,X2,X3)),hAPP(nat,X1,X2,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_3002]) ).

cnf(c_0_3003_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,X2,X3)),hAPP(nat,X1,X2,X4)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,X2,sk1_esk89_4(X1,X3,X4,X2))),hAPP(nat,X1,X2,hAPP(nat,nat,suc,sk1_esk89_4(X1,X3,X4,X2)))))
    | ~ order(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3003]) ).

cnf(c_0_3003_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X4))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,X2,X3)),hAPP(nat,X1,X2,X4)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,X2,sk1_esk89_4(X1,X3,X4,X2))),hAPP(nat,X1,X2,hAPP(nat,nat,suc,sk1_esk89_4(X1,X3,X4,X2)))))
    | ~ order(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3003]) ).

cnf(c_0_3003_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,X2,sk1_esk89_4(X1,X3,X4,X2))),hAPP(nat,X1,X2,hAPP(nat,nat,suc,sk1_esk89_4(X1,X3,X4,X2)))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X4))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,X2,X3)),hAPP(nat,X1,X2,X4)))
    | ~ order(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3003]) ).

cnf(c_0_3003_3,axiom,
    ( ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,X2,sk1_esk89_4(X1,X3,X4,X2))),hAPP(nat,X1,X2,hAPP(nat,nat,suc,sk1_esk89_4(X1,X3,X4,X2)))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X4))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(nat,X1,X2,X3)),hAPP(nat,X1,X2,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_3003]) ).

cnf(c_0_3004_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3004]) ).

cnf(c_0_3004_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3004]) ).

cnf(c_0_3004_2,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3004]) ).

cnf(c_0_3004_3,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_3004]) ).

cnf(c_0_3005_0,axiom,
    ( hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),hAPP(fun(nat,bool),nat,finite_card(nat),X1))) = X1
    | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),X1),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),hAPP(fun(nat,bool),nat,finite_card(nat),X1))))) ),
    inference(literals_permutation,[status(thm)],[c_0_3005]) ).

cnf(c_0_3005_1,axiom,
    ( ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),X1),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),hAPP(fun(nat,bool),nat,finite_card(nat),X1)))))
    | hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),hAPP(fun(nat,bool),nat,finite_card(nat),X1))) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_3005]) ).

cnf(c_0_3006_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X2)),hAPP(fun(X3,bool),nat,finite_card(X3),X4)))
    | ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X5),X2))
    | ~ hBOOL(hAPP(fun(fun(X1,X3),bool),bool,hAPP(fun(X1,X3),fun(fun(fun(X1,X3),bool),bool),member(fun(X1,X3)),X5),hAPP(fun(X1,fun(X3,bool)),fun(fun(X1,X3),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X3,bool)),fun(fun(X1,X3),bool)),pi(X1,X3),X2),hAPP(fun(X3,bool),fun(X1,fun(X3,bool)),combk(fun(X3,bool),X1),X4)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3006]) ).

cnf(c_0_3006_1,axiom,
    ( ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X4))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X2)),hAPP(fun(X3,bool),nat,finite_card(X3),X4)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X5),X2))
    | ~ hBOOL(hAPP(fun(fun(X1,X3),bool),bool,hAPP(fun(X1,X3),fun(fun(fun(X1,X3),bool),bool),member(fun(X1,X3)),X5),hAPP(fun(X1,fun(X3,bool)),fun(fun(X1,X3),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X3,bool)),fun(fun(X1,X3),bool)),pi(X1,X3),X2),hAPP(fun(X3,bool),fun(X1,fun(X3,bool)),combk(fun(X3,bool),X1),X4)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3006]) ).

cnf(c_0_3006_2,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X5),X2))
    | ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X4))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X2)),hAPP(fun(X3,bool),nat,finite_card(X3),X4)))
    | ~ hBOOL(hAPP(fun(fun(X1,X3),bool),bool,hAPP(fun(X1,X3),fun(fun(fun(X1,X3),bool),bool),member(fun(X1,X3)),X5),hAPP(fun(X1,fun(X3,bool)),fun(fun(X1,X3),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X3,bool)),fun(fun(X1,X3),bool)),pi(X1,X3),X2),hAPP(fun(X3,bool),fun(X1,fun(X3,bool)),combk(fun(X3,bool),X1),X4)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3006]) ).

cnf(c_0_3006_3,axiom,
    ( ~ hBOOL(hAPP(fun(fun(X1,X3),bool),bool,hAPP(fun(X1,X3),fun(fun(fun(X1,X3),bool),bool),member(fun(X1,X3)),X5),hAPP(fun(X1,fun(X3,bool)),fun(fun(X1,X3),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X3,bool)),fun(fun(X1,X3),bool)),pi(X1,X3),X2),hAPP(fun(X3,bool),fun(X1,fun(X3,bool)),combk(fun(X3,bool),X1),X4))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X5),X2))
    | ~ hBOOL(hAPP(fun(X3,bool),bool,finite_finite_1(X3),X4))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X2)),hAPP(fun(X3,bool),nat,finite_card(X3),X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_3006]) ).

cnf(c_0_3007_0,axiom,
    ( ti(X1,X2) = ti(X1,X3)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(fun(X4,bool),fun(X1,bool),hAPP(fun(X4,X1),fun(fun(X4,bool),fun(X1,bool)),image(X4,X1),X5),X6)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X4,bool),fun(X1,bool),hAPP(fun(X4,X1),fun(fun(X4,bool),fun(X1,bool)),image(X4,X1),X5),X6)))
    | hAPP(X1,X4,hAPP(fun(X4,X1),fun(X1,X4),hAPP(fun(X4,bool),fun(fun(X4,X1),fun(X1,X4)),hilbert_inv_into(X4,X1),X6),X5),X2) != hAPP(X1,X4,hAPP(fun(X4,X1),fun(X1,X4),hAPP(fun(X4,bool),fun(fun(X4,X1),fun(X1,X4)),hilbert_inv_into(X4,X1),X6),X5),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3007]) ).

cnf(c_0_3007_1,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(fun(X4,bool),fun(X1,bool),hAPP(fun(X4,X1),fun(fun(X4,bool),fun(X1,bool)),image(X4,X1),X5),X6)))
    | ti(X1,X2) = ti(X1,X3)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X4,bool),fun(X1,bool),hAPP(fun(X4,X1),fun(fun(X4,bool),fun(X1,bool)),image(X4,X1),X5),X6)))
    | hAPP(X1,X4,hAPP(fun(X4,X1),fun(X1,X4),hAPP(fun(X4,bool),fun(fun(X4,X1),fun(X1,X4)),hilbert_inv_into(X4,X1),X6),X5),X2) != hAPP(X1,X4,hAPP(fun(X4,X1),fun(X1,X4),hAPP(fun(X4,bool),fun(fun(X4,X1),fun(X1,X4)),hilbert_inv_into(X4,X1),X6),X5),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3007]) ).

cnf(c_0_3007_2,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X4,bool),fun(X1,bool),hAPP(fun(X4,X1),fun(fun(X4,bool),fun(X1,bool)),image(X4,X1),X5),X6)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(fun(X4,bool),fun(X1,bool),hAPP(fun(X4,X1),fun(fun(X4,bool),fun(X1,bool)),image(X4,X1),X5),X6)))
    | ti(X1,X2) = ti(X1,X3)
    | hAPP(X1,X4,hAPP(fun(X4,X1),fun(X1,X4),hAPP(fun(X4,bool),fun(fun(X4,X1),fun(X1,X4)),hilbert_inv_into(X4,X1),X6),X5),X2) != hAPP(X1,X4,hAPP(fun(X4,X1),fun(X1,X4),hAPP(fun(X4,bool),fun(fun(X4,X1),fun(X1,X4)),hilbert_inv_into(X4,X1),X6),X5),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3007]) ).

cnf(c_0_3007_3,axiom,
    ( hAPP(X1,X4,hAPP(fun(X4,X1),fun(X1,X4),hAPP(fun(X4,bool),fun(fun(X4,X1),fun(X1,X4)),hilbert_inv_into(X4,X1),X6),X5),X2) != hAPP(X1,X4,hAPP(fun(X4,X1),fun(X1,X4),hAPP(fun(X4,bool),fun(fun(X4,X1),fun(X1,X4)),hilbert_inv_into(X4,X1),X6),X5),X3)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X4,bool),fun(X1,bool),hAPP(fun(X4,X1),fun(fun(X4,bool),fun(X1,bool)),image(X4,X1),X5),X6)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),hAPP(fun(X4,bool),fun(X1,bool),hAPP(fun(X4,X1),fun(fun(X4,bool),fun(X1,bool)),image(X4,X1),X5),X6)))
    | ti(X1,X2) = ti(X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3007]) ).

cnf(c_0_3008_0,axiom,
    ( hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),member(product_prod(X1,X2)),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X5),X6)),X4))
    | ti(fun(product_prod(X1,X2),bool),X3) != ti(fun(product_prod(X1,X2),bool),X4)
    | ~ hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),member(product_prod(X1,X2)),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X5),X6)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3008]) ).

cnf(c_0_3008_1,axiom,
    ( ti(fun(product_prod(X1,X2),bool),X3) != ti(fun(product_prod(X1,X2),bool),X4)
    | hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),member(product_prod(X1,X2)),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X5),X6)),X4))
    | ~ hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),member(product_prod(X1,X2)),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X5),X6)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3008]) ).

cnf(c_0_3008_2,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),member(product_prod(X1,X2)),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X5),X6)),X3))
    | ti(fun(product_prod(X1,X2),bool),X3) != ti(fun(product_prod(X1,X2),bool),X4)
    | hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),member(product_prod(X1,X2)),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X5),X6)),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3008]) ).

cnf(c_0_3009_0,axiom,
    ( hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),member(product_prod(X1,X2)),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X5),X6)),X3))
    | ti(fun(product_prod(X1,X2),bool),X3) != ti(fun(product_prod(X1,X2),bool),X4)
    | ~ hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),member(product_prod(X1,X2)),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X5),X6)),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3009]) ).

cnf(c_0_3009_1,axiom,
    ( ti(fun(product_prod(X1,X2),bool),X3) != ti(fun(product_prod(X1,X2),bool),X4)
    | hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),member(product_prod(X1,X2)),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X5),X6)),X3))
    | ~ hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),member(product_prod(X1,X2)),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X5),X6)),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3009]) ).

cnf(c_0_3009_2,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),member(product_prod(X1,X2)),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X5),X6)),X4))
    | ti(fun(product_prod(X1,X2),bool),X3) != ti(fun(product_prod(X1,X2),bool),X4)
    | hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),member(product_prod(X1,X2)),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X5),X6)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3009]) ).

cnf(c_0_3010_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X2,X1,X3,X4)),X5))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X4),X6))
    | ~ hBOOL(hAPP(fun(fun(X2,X1),bool),bool,hAPP(fun(X2,X1),fun(fun(fun(X2,X1),bool),bool),member(fun(X2,X1)),X3),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,X1),bool),hAPP(fun(X2,bool),fun(fun(X2,fun(X1,bool)),fun(fun(X2,X1),bool)),pi(X2,X1),X6),hAPP(fun(X1,bool),fun(X2,fun(X1,bool)),combk(fun(X1,bool),X2),X5)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3010]) ).

cnf(c_0_3010_1,axiom,
    ( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X4),X6))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X2,X1,X3,X4)),X5))
    | ~ hBOOL(hAPP(fun(fun(X2,X1),bool),bool,hAPP(fun(X2,X1),fun(fun(fun(X2,X1),bool),bool),member(fun(X2,X1)),X3),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,X1),bool),hAPP(fun(X2,bool),fun(fun(X2,fun(X1,bool)),fun(fun(X2,X1),bool)),pi(X2,X1),X6),hAPP(fun(X1,bool),fun(X2,fun(X1,bool)),combk(fun(X1,bool),X2),X5)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3010]) ).

cnf(c_0_3010_2,axiom,
    ( ~ hBOOL(hAPP(fun(fun(X2,X1),bool),bool,hAPP(fun(X2,X1),fun(fun(fun(X2,X1),bool),bool),member(fun(X2,X1)),X3),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,X1),bool),hAPP(fun(X2,bool),fun(fun(X2,fun(X1,bool)),fun(fun(X2,X1),bool)),pi(X2,X1),X6),hAPP(fun(X1,bool),fun(X2,fun(X1,bool)),combk(fun(X1,bool),X2),X5))))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X4),X6))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X2,X1,X3,X4)),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_3010]) ).

cnf(c_0_3011_0,axiom,
    ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(fun(X1,X2),bool),fun(fun(fun(X1,X2),bool),bool),ord_less_eq(fun(fun(X1,X2),bool)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X3),X4)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X5),X4)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X5),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3011]) ).

cnf(c_0_3011_1,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X5),X3))
    | hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(fun(X1,X2),bool),fun(fun(fun(X1,X2),bool),bool),ord_less_eq(fun(fun(X1,X2),bool)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X3),X4)),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X5),X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_3011]) ).

cnf(c_0_3012_0,axiom,
    ( ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X2)),X1))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),X1))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X1),arrow_2064824852le_Lin)) ),
    inference(literals_permutation,[status(thm)],[c_0_3012]) ).

cnf(c_0_3012_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X2)),X1))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),X1))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X1),arrow_2064824852le_Lin)) ),
    inference(literals_permutation,[status(thm)],[c_0_3012]) ).

cnf(c_0_3012_2,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),X1))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X2)),X1))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3)
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X1),arrow_2064824852le_Lin)) ),
    inference(literals_permutation,[status(thm)],[c_0_3012]) ).

cnf(c_0_3012_3,axiom,
    ( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X1),arrow_2064824852le_Lin))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X2),X3)),X1))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X3),X2)),X1))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3012]) ).

cnf(c_0_3013_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_3013]) ).

cnf(c_0_3013_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_3013]) ).

cnf(c_0_3013_2,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_3013]) ).

cnf(c_0_3013_3,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_3013]) ).

cnf(c_0_3014_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(X1,bool)),combc(X1,fun(X1,bool),bool),member(X1)),X2)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(X1,bool)),combc(X1,fun(X1,bool),bool),member(X1)),X3)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3014]) ).

cnf(c_0_3014_1,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(X1,bool)),combc(X1,fun(X1,bool),bool),member(X1)),X2)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(X1,bool)),combc(X1,fun(X1,bool),bool),member(X1)),X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_3014]) ).

cnf(c_0_3015_0,axiom,
    ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sk1_esk12_1(X1)),sk1_esk13_1(X1))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,sk1_esk11_1(X1))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sk1_esk12_1(X1)),sk1_esk13_1(X1))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,sk1_esk10_1(X1)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3015]) ).

cnf(c_0_3015_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sk1_esk12_1(X1)),sk1_esk13_1(X1))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,sk1_esk11_1(X1))))
    | hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sk1_esk12_1(X1)),sk1_esk13_1(X1))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,sk1_esk10_1(X1)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3015]) ).

cnf(c_0_3015_2,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sk1_esk12_1(X1)),sk1_esk13_1(X1))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,sk1_esk10_1(X1))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sk1_esk12_1(X1)),sk1_esk13_1(X1))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,sk1_esk11_1(X1))))
    | hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_3015]) ).

cnf(c_0_3016_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,X1,X2)),X3)),hAPP(nat,nat,X1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3))))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sk1_esk61_3(X2,X3,X1)),sk1_esk62_3(X2,X3,X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_3016]) ).

cnf(c_0_3016_1,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sk1_esk61_3(X2,X3,X1)),sk1_esk62_3(X2,X3,X1)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,X1,X2)),X3)),hAPP(nat,nat,X1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3016]) ).

cnf(c_0_3017_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3017]) ).

cnf(c_0_3017_1,axiom,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3017]) ).

cnf(c_0_3017_2,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3017]) ).

cnf(c_0_3017_3,axiom,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3017]) ).

cnf(c_0_3017_4,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_3017]) ).

cnf(c_0_3018_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_3018]) ).

cnf(c_0_3018_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_3018]) ).

cnf(c_0_3018_2,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_3018]) ).

cnf(c_0_3018_3,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_3018]) ).

cnf(c_0_3019_0,axiom,
    ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X3),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X4),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),X5))))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk65_5(X2,X1,X3,X5,X4)),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3019]) ).

cnf(c_0_3019_1,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk65_5(X2,X1,X3,X5,X4)),X4))
    | hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X3),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X4),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),X5)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3019]) ).

cnf(c_0_3020_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X2))
    | ~ linorder(X1)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_3020]) ).

cnf(c_0_3020_1,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X2))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ linorder(X1)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_3020]) ).

cnf(c_0_3020_2,axiom,
    ( ~ linorder(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X2))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_3020]) ).

cnf(c_0_3020_3,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5)))
    | ~ linorder(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X2))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3020]) ).

cnf(c_0_3021_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
    | ~ linorder(X1)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_3021]) ).

cnf(c_0_3021_1,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ linorder(X1)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_3021]) ).

cnf(c_0_3021_2,axiom,
    ( ~ linorder(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_3021]) ).

cnf(c_0_3021_3,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X3)),hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5)))
    | ~ linorder(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3021]) ).

cnf(c_0_3022_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X4))),hAPP(fun(X2,bool),nat,finite_card(X2),X4)))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3022]) ).

cnf(c_0_3022_1,axiom,
    ( ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X4))),hAPP(fun(X2,bool),nat,finite_card(X2),X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_3022]) ).

cnf(c_0_3023_0,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X3),X4)))
    | ti(arrow_490897120le_alt,X1) != ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X2) != ti(arrow_490897120le_alt,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_3023]) ).

cnf(c_0_3023_1,axiom,
    ( ti(arrow_490897120le_alt,X1) != ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X3),X4)))
    | ti(arrow_490897120le_alt,X2) != ti(arrow_490897120le_alt,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_3023]) ).

cnf(c_0_3023_2,axiom,
    ( ti(arrow_490897120le_alt,X2) != ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) != ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X3),X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_3023]) ).

cnf(c_0_3024_0,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X3),X4)))
    | ti(arrow_490897120le_alt,X1) != ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X1) != ti(arrow_490897120le_alt,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_3024]) ).

cnf(c_0_3024_1,axiom,
    ( ti(arrow_490897120le_alt,X1) != ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X3),X4)))
    | ti(arrow_490897120le_alt,X1) != ti(arrow_490897120le_alt,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_3024]) ).

cnf(c_0_3024_2,axiom,
    ( ti(arrow_490897120le_alt,X1) != ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) != ti(arrow_490897120le_alt,X2)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X3),X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_3024]) ).

cnf(c_0_3025_0,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X3),X4)))
    | ti(arrow_490897120le_alt,X1) != ti(arrow_490897120le_alt,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_3025]) ).

cnf(c_0_3025_1,axiom,
    ( ti(arrow_490897120le_alt,X1) != ti(arrow_490897120le_alt,X4)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X3),X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_3025]) ).

cnf(c_0_3026_0,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X3),X4)))
    | ti(arrow_490897120le_alt,X2) != ti(arrow_490897120le_alt,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_3026]) ).

cnf(c_0_3026_1,axiom,
    ( ti(arrow_490897120le_alt,X2) != ti(arrow_490897120le_alt,X4)
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X3),X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_3026]) ).

cnf(c_0_3027_0,axiom,
    ( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X2),X3) = ti(fun(X1,bool),X3)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X2),X3)),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3027]) ).

cnf(c_0_3027_1,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X2),X3))
    | hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X2),X3) = ti(fun(X1,bool),X3)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X2),X3)),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3027]) ).

cnf(c_0_3027_2,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X2),X3)),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X2),X3))
    | hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X2),X3) = ti(fun(X1,bool),X3)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3027]) ).

cnf(c_0_3027_3,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X2),X3)),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X2),X3))
    | hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X2),X3) = ti(fun(X1,bool),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3027]) ).

cnf(c_0_3028_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_3028]) ).

cnf(c_0_3028_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_3028]) ).

cnf(c_0_3028_2,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_3028]) ).

cnf(c_0_3028_3,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_3028]) ).

cnf(c_0_3029_0,axiom,
    ( hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X4)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X5)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),top_top(fun(X1,bool))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_3029]) ).

cnf(c_0_3029_1,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),top_top(fun(X1,bool))))
    | hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X4)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X5)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_3029]) ).

cnf(c_0_3029_2,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X5))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),top_top(fun(X1,bool))))
    | hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X4)),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_3029]) ).

cnf(c_0_3030_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X2,X1,X3,X4)),hAPP(X2,fun(X1,bool),X5,X4)))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X4),X6))
    | ~ hBOOL(hAPP(fun(fun(X2,X1),bool),bool,hAPP(fun(X2,X1),fun(fun(fun(X2,X1),bool),bool),member(fun(X2,X1)),X3),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,X1),bool),hAPP(fun(X2,bool),fun(fun(X2,fun(X1,bool)),fun(fun(X2,X1),bool)),pi(X2,X1),X6),X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_3030]) ).

cnf(c_0_3030_1,axiom,
    ( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X4),X6))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X2,X1,X3,X4)),hAPP(X2,fun(X1,bool),X5,X4)))
    | ~ hBOOL(hAPP(fun(fun(X2,X1),bool),bool,hAPP(fun(X2,X1),fun(fun(fun(X2,X1),bool),bool),member(fun(X2,X1)),X3),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,X1),bool),hAPP(fun(X2,bool),fun(fun(X2,fun(X1,bool)),fun(fun(X2,X1),bool)),pi(X2,X1),X6),X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_3030]) ).

cnf(c_0_3030_2,axiom,
    ( ~ hBOOL(hAPP(fun(fun(X2,X1),bool),bool,hAPP(fun(X2,X1),fun(fun(fun(X2,X1),bool),bool),member(fun(X2,X1)),X3),hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,X1),bool),hAPP(fun(X2,bool),fun(fun(X2,fun(X1,bool)),fun(fun(X2,X1),bool)),pi(X2,X1),X6),X5)))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X4),X6))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X2,X1,X3,X4)),hAPP(X2,fun(X1,bool),X5,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_3030]) ).

cnf(c_0_3031_0,axiom,
    ( hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),hAPP(X1,X4,X5,X2)),hAPP(X1,fun(X4,bool),X6,X2)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
    | ~ hBOOL(hAPP(fun(fun(X1,X4),bool),bool,hAPP(fun(X1,X4),fun(fun(fun(X1,X4),bool),bool),member(fun(X1,X4)),X5),hAPP(fun(X1,fun(X4,bool)),fun(fun(X1,X4),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X4,bool)),fun(fun(X1,X4),bool)),pi(X1,X4),X3),X6))) ),
    inference(literals_permutation,[status(thm)],[c_0_3031]) ).

cnf(c_0_3031_1,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
    | hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),hAPP(X1,X4,X5,X2)),hAPP(X1,fun(X4,bool),X6,X2)))
    | ~ hBOOL(hAPP(fun(fun(X1,X4),bool),bool,hAPP(fun(X1,X4),fun(fun(fun(X1,X4),bool),bool),member(fun(X1,X4)),X5),hAPP(fun(X1,fun(X4,bool)),fun(fun(X1,X4),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X4,bool)),fun(fun(X1,X4),bool)),pi(X1,X4),X3),X6))) ),
    inference(literals_permutation,[status(thm)],[c_0_3031]) ).

cnf(c_0_3031_2,axiom,
    ( ~ hBOOL(hAPP(fun(fun(X1,X4),bool),bool,hAPP(fun(X1,X4),fun(fun(fun(X1,X4),bool),bool),member(fun(X1,X4)),X5),hAPP(fun(X1,fun(X4,bool)),fun(fun(X1,X4),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X4,bool)),fun(fun(X1,X4),bool)),pi(X1,X4),X3),X6)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
    | hBOOL(hAPP(fun(X4,bool),bool,hAPP(X4,fun(fun(X4,bool),bool),member(X4),hAPP(X1,X4,X5,X2)),hAPP(X1,fun(X4,bool),X6,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_3031]) ).

cnf(c_0_3032_0,axiom,
    ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),sk1_esk102_5(X1,X3,X2,X4,X5)),X5))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_3032]) ).

cnf(c_0_3032_1,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5)))
    | hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),sk1_esk102_5(X1,X3,X2,X4,X5)),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_3032]) ).

cnf(c_0_3033_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X4)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X5)))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less(fun(X2,bool)),X4),X5))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),inj_on(X2,X1),X3),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_3033]) ).

cnf(c_0_3033_1,axiom,
    ( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less(fun(X2,bool)),X4),X5))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X4)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X5)))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),inj_on(X2,X1),X3),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_3033]) ).

cnf(c_0_3033_2,axiom,
    ( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),inj_on(X2,X1),X3),X5))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less(fun(X2,bool)),X4),X5))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X4)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_3033]) ).

cnf(c_0_3034_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(bool,bool),fun(fun(X1,bool),fun(X1,bool)),combb(bool,bool,X1),fNot),X2)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3034]) ).

cnf(c_0_3034_1,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2)))
    | hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(bool,bool),fun(fun(X1,bool),fun(X1,bool)),combb(bool,bool,X1),fNot),X2)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3034]) ).

cnf(c_0_3034_2,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(bool,bool),fun(fun(X1,bool),fun(X1,bool)),combb(bool,bool,X1),fNot),X2))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2)))
    | hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3034]) ).

cnf(c_0_3035_0,axiom,
    ( hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),sk1_esk101_5(X1,X3,X2,X4,X5)),X5))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_3035]) ).

cnf(c_0_3035_1,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5)))
    | hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),sk1_esk101_5(X1,X3,X2,X4,X5)),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_3035]) ).

cnf(c_0_3036_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(product_prod(X2,X1),bool),fun(X2,fun(X1,bool)),in_rel(X2,X1),X3),X4),X5))
    | ~ hBOOL(hAPP(fun(product_prod(X2,X1),bool),bool,hAPP(product_prod(X2,X1),fun(fun(product_prod(X2,X1),bool),bool),member(product_prod(X2,X1)),hAPP(X1,product_prod(X2,X1),hAPP(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),X4),X5)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3036]) ).

cnf(c_0_3036_1,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(X2,X1),bool),bool,hAPP(product_prod(X2,X1),fun(fun(product_prod(X2,X1),bool),bool),member(product_prod(X2,X1)),hAPP(X1,product_prod(X2,X1),hAPP(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),X4),X5)),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),hAPP(fun(product_prod(X2,X1),bool),fun(X2,fun(X1,bool)),in_rel(X2,X1),X3),X4),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_3036]) ).

cnf(c_0_3037_0,axiom,
    ( hBOOL(hAPP(fun(fun(X1,bool),bool),bool,finite_finite_1(fun(X1,bool)),hAPP(fun(fun(X1,bool),bool),fun(fun(X1,bool),bool),collect(fun(X1,bool)),hAPP(fun(X1,bool),fun(fun(X1,bool),bool),hAPP(fun(fun(X1,bool),fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(fun(X1,bool),bool)),combc(fun(X1,bool),fun(X1,bool),bool),ord_less_eq(fun(X1,bool))),X2))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3037]) ).

cnf(c_0_3037_1,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | hBOOL(hAPP(fun(fun(X1,bool),bool),bool,finite_finite_1(fun(X1,bool)),hAPP(fun(fun(X1,bool),bool),fun(fun(X1,bool),bool),collect(fun(X1,bool)),hAPP(fun(X1,bool),fun(fun(X1,bool),bool),hAPP(fun(fun(X1,bool),fun(fun(X1,bool),bool)),fun(fun(X1,bool),fun(fun(X1,bool),bool)),combc(fun(X1,bool),fun(X1,bool),bool),ord_less_eq(fun(X1,bool))),X2)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3037]) ).

cnf(c_0_3038_0,axiom,
    ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X3),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X4),X5)))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk68_5(X2,X1,X3,X5,X4)),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3038]) ).

cnf(c_0_3038_1,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk68_5(X2,X1,X3,X5,X4)),X4))
    | hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X3),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X4),X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_3038]) ).

cnf(c_0_3039_0,axiom,
    ( hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X3),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X4),X5)))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk33_5(X2,X1,X3,X5,X4)),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3039]) ).

cnf(c_0_3039_1,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk33_5(X2,X1,X3,X5,X4)),X4))
    | hBOOL(hAPP(fun(fun(X1,X2),bool),bool,hAPP(fun(X1,X2),fun(fun(fun(X1,X2),bool),bool),member(fun(X1,X2)),X3),hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X4),X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_3039]) ).

cnf(c_0_3040_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,fun(X2,X3)),fun(fun(X1,bool),bool),inj_on(X1,fun(X2,X3)),hAPP(fun(X1,X3),fun(X1,fun(X2,X3)),hAPP(fun(X3,fun(X2,X3)),fun(fun(X1,X3),fun(X1,fun(X2,X3))),combb(X3,fun(X2,X3),X1),combk(X3,X2)),X4)),top_top(fun(X1,bool))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X4),top_top(fun(X1,bool)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3040]) ).

cnf(c_0_3040_1,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X4),top_top(fun(X1,bool))))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,fun(X2,X3)),fun(fun(X1,bool),bool),inj_on(X1,fun(X2,X3)),hAPP(fun(X1,X3),fun(X1,fun(X2,X3)),hAPP(fun(X3,fun(X2,X3)),fun(fun(X1,X3),fun(X1,fun(X2,X3))),combb(X3,fun(X2,X3),X1),combk(X3,X2)),X4)),top_top(fun(X1,bool)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3040]) ).

cnf(c_0_3041_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_3041]) ).

cnf(c_0_3041_1,axiom,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_3041]) ).

cnf(c_0_3041_2,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_3041]) ).

cnf(c_0_3041_3,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_3041]) ).

cnf(c_0_3041_4,axiom,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_3041]) ).

cnf(c_0_3042_0,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_3042]) ).

cnf(c_0_3042_1,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_3042]) ).

cnf(c_0_3042_2,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_3042]) ).

cnf(c_0_3043_0,axiom,
    ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,X1))
    | ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sk1_esk16_1(X1)),sk1_esk17_1(X1))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,sk1_esk15_1(X1)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3043]) ).

cnf(c_0_3043_1,axiom,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sk1_esk16_1(X1)),sk1_esk17_1(X1))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,sk1_esk15_1(X1))))
    | hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_3043]) ).

cnf(c_0_3044_0,axiom,
    ( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X1),X2)),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X1),arrow_2064824852le_Lin)) ),
    inference(literals_permutation,[status(thm)],[c_0_3044]) ).

cnf(c_0_3044_1,axiom,
    ( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X1),arrow_2064824852le_Lin))
    | hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X1),X2)),arrow_2064824852le_Lin)) ),
    inference(literals_permutation,[status(thm)],[c_0_3044]) ).

cnf(c_0_3045_0,axiom,
    ( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X1),X2)),arrow_2064824852le_Lin))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X1),arrow_2064824852le_Lin)) ),
    inference(literals_permutation,[status(thm)],[c_0_3045]) ).

cnf(c_0_3045_1,axiom,
    ( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X1),arrow_2064824852le_Lin))
    | hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X1),X2)),arrow_2064824852le_Lin)) ),
    inference(literals_permutation,[status(thm)],[c_0_3045]) ).

cnf(c_0_3046_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_3046]) ).

cnf(c_0_3046_1,axiom,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_3046]) ).

cnf(c_0_3046_2,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_3046]) ).

cnf(c_0_3046_3,axiom,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_3046]) ).

cnf(c_0_3046_4,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_3046]) ).

cnf(c_0_3047_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ ordere236663937imp_le(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_3047]) ).

cnf(c_0_3047_1,axiom,
    ( ~ ordere236663937imp_le(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_3047]) ).

cnf(c_0_3047_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)))
    | ~ ordere236663937imp_le(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3047]) ).

cnf(c_0_3048_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ ordere236663937imp_le(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_3048]) ).

cnf(c_0_3048_1,axiom,
    ( ~ ordere236663937imp_le(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_3048]) ).

cnf(c_0_3048_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)))
    | ~ ordere236663937imp_le(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3048]) ).

cnf(c_0_3049_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)))
    | ~ ordere236663937imp_le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3049]) ).

cnf(c_0_3049_1,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ ordere236663937imp_le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3049]) ).

cnf(c_0_3049_2,axiom,
    ( ~ ordere236663937imp_le(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3049]) ).

cnf(c_0_3050_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)))
    | ~ ordere236663937imp_le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3050]) ).

cnf(c_0_3050_1,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ ordere236663937imp_le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3050]) ).

cnf(c_0_3050_2,axiom,
    ( ~ ordere236663937imp_le(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3050]) ).

cnf(c_0_3051_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ ordere236663937imp_le(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_3051]) ).

cnf(c_0_3051_1,axiom,
    ( ~ ordere236663937imp_le(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_3051]) ).

cnf(c_0_3051_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)))
    | ~ ordere236663937imp_le(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3051]) ).

cnf(c_0_3052_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ ordere236663937imp_le(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_3052]) ).

cnf(c_0_3052_1,axiom,
    ( ~ ordere236663937imp_le(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_3052]) ).

cnf(c_0_3052_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)))
    | ~ ordere236663937imp_le(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3052]) ).

cnf(c_0_3053_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)))
    | ~ ordere236663937imp_le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3053]) ).

cnf(c_0_3053_1,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ ordere236663937imp_le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3053]) ).

cnf(c_0_3053_2,axiom,
    ( ~ ordere236663937imp_le(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3053]) ).

cnf(c_0_3054_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)))
    | ~ ordere236663937imp_le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3054]) ).

cnf(c_0_3054_1,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ ordere236663937imp_le(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3054]) ).

cnf(c_0_3054_2,axiom,
    ( ~ ordere236663937imp_le(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X2)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3054]) ).

cnf(c_0_3055_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X4)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X5)))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X4),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_3055]) ).

cnf(c_0_3055_1,axiom,
    ( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,bool),fun(fun(X2,bool),bool),ord_less_eq(fun(X2,bool)),X4),X5))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X4)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_3055]) ).

cnf(c_0_3056_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_3056]) ).

cnf(c_0_3056_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X2)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3056]) ).

cnf(c_0_3057_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_3057]) ).

cnf(c_0_3057_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X2)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3057]) ).

cnf(c_0_3058_0,axiom,
    ( hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less_eq(fun(X1,X2)),X3),X4))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,sk1_esk39_4(X1,X2,X3,X4))),hAPP(X1,X2,X4,sk1_esk39_4(X1,X2,X3,X4))))
    | ~ ord(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3058]) ).

cnf(c_0_3058_1,axiom,
    ( ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,sk1_esk39_4(X1,X2,X3,X4))),hAPP(X1,X2,X4,sk1_esk39_4(X1,X2,X3,X4))))
    | hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less_eq(fun(X1,X2)),X3),X4))
    | ~ ord(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3058]) ).

cnf(c_0_3058_2,axiom,
    ( ~ ord(X2)
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less_eq(X2),hAPP(X1,X2,X3,sk1_esk39_4(X1,X2,X3,X4))),hAPP(X1,X2,X4,sk1_esk39_4(X1,X2,X3,X4))))
    | hBOOL(hAPP(fun(X1,X2),bool,hAPP(fun(X1,X2),fun(fun(X1,X2),bool),ord_less_eq(fun(X1,X2)),X3),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3058]) ).

cnf(c_0_3059_0,axiom,
    ( hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X4))
    | ~ ord(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X3,sk1_esk29_4(X2,X1,X3,X4))),hAPP(X2,X1,X4,sk1_esk29_4(X2,X1,X3,X4)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3059]) ).

cnf(c_0_3059_1,axiom,
    ( ~ ord(X1)
    | hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X3,sk1_esk29_4(X2,X1,X3,X4))),hAPP(X2,X1,X4,sk1_esk29_4(X2,X1,X3,X4)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3059]) ).

cnf(c_0_3059_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X3,sk1_esk29_4(X2,X1,X3,X4))),hAPP(X2,X1,X4,sk1_esk29_4(X2,X1,X3,X4))))
    | ~ ord(X1)
    | hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3059]) ).

cnf(c_0_3060_0,axiom,
    ( hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),member(product_prod(X1,X2)),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X3),X4)),X5))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),hAPP(fun(product_prod(X1,X2),bool),fun(X1,fun(X2,bool)),in_rel(X1,X2),X5),X3),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3060]) ).

cnf(c_0_3060_1,axiom,
    ( ~ hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),hAPP(fun(product_prod(X1,X2),bool),fun(X1,fun(X2,bool)),in_rel(X1,X2),X5),X3),X4))
    | hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,hAPP(product_prod(X1,X2),fun(fun(product_prod(X1,X2),bool),bool),member(product_prod(X1,X2)),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X3),X4)),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_3060]) ).

cnf(c_0_3061_0,axiom,
    ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),combk(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),arrow_660593299e_indi),X1)),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X1),arrow_2064824852le_Lin)) ),
    inference(literals_permutation,[status(thm)],[c_0_3061]) ).

cnf(c_0_3061_1,axiom,
    ( ~ hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),X1),arrow_2064824852le_Lin))
    | hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),combk(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),arrow_660593299e_indi),X1)),arrow_1111136790e_Prof)) ),
    inference(literals_permutation,[status(thm)],[c_0_3061]) ).

cnf(c_0_3062_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_3062]) ).

cnf(c_0_3062_1,axiom,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_3062]) ).

cnf(c_0_3062_2,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_3062]) ).

cnf(c_0_3062_3,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_3062]) ).

cnf(c_0_3062_4,axiom,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n)) ),
    inference(literals_permutation,[status(thm)],[c_0_3062]) ).

cnf(c_0_3063_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk71_5(X2,X1,X3,X4,X5)),X5))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X4),X5))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_3063]) ).

cnf(c_0_3063_1,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X4),X5))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk71_5(X2,X1,X3,X4,X5)),X5))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_3063]) ).

cnf(c_0_3063_2,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X5))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X4),X5))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk71_5(X2,X1,X3,X4,X5)),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_3063]) ).

cnf(c_0_3064_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk71_5(X2,X1,X3,X4,X5)),X5))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X5))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X4),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_3064]) ).

cnf(c_0_3064_1,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X5))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk71_5(X2,X1,X3,X4,X5)),X5))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X4),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_3064]) ).

cnf(c_0_3064_2,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X4),X5))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X5))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk71_5(X2,X1,X3,X4,X5)),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_3064]) ).

cnf(c_0_3065_0,axiom,
    ( hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X2) = hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X2,X3)
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X2),arrow_1111136790e_Prof))
    | ~ hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,X1),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3065]) ).

cnf(c_0_3065_1,axiom,
    ( ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X2),arrow_1111136790e_Prof))
    | hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X2) = hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X2,X3)
    | ~ hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,X1),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3065]) ).

cnf(c_0_3065_2,axiom,
    ( ~ hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,X1),X3))
    | ~ hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),X2),arrow_1111136790e_Prof))
    | hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,X2) = hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X2,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3065]) ).

cnf(c_0_3066_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X5)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | ~ ordere223160158up_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3066]) ).

cnf(c_0_3066_1,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X5)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | ~ ordere223160158up_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3066]) ).

cnf(c_0_3066_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X5)))
    | ~ ordere223160158up_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3066]) ).

cnf(c_0_3066_3,axiom,
    ( ~ ordere223160158up_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_3066]) ).

cnf(c_0_3067_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X5)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | ~ ordere779506340up_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3067]) ).

cnf(c_0_3067_1,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X5)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | ~ ordere779506340up_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3067]) ).

cnf(c_0_3067_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X5)))
    | ~ ordere779506340up_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3067]) ).

cnf(c_0_3067_3,axiom,
    ( ~ ordere779506340up_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_3067]) ).

cnf(c_0_3068_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X5)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | ~ ordere223160158up_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3068]) ).

cnf(c_0_3068_1,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X5)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | ~ ordere223160158up_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3068]) ).

cnf(c_0_3068_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X5)))
    | ~ ordere223160158up_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3068]) ).

cnf(c_0_3068_3,axiom,
    ( ~ ordere223160158up_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X5))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_3068]) ).

cnf(c_0_3069_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X5)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | ~ ordere223160158up_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3069]) ).

cnf(c_0_3069_1,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X5)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | ~ ordere223160158up_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3069]) ).

cnf(c_0_3069_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X5)))
    | ~ ordere223160158up_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3069]) ).

cnf(c_0_3069_3,axiom,
    ( ~ ordere223160158up_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X5))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_3069]) ).

cnf(c_0_3070_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X1,X2)),hAPP(nat,nat,X1,X3)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,X1,sk1_esk63_3(X2,X3,X1))),hAPP(nat,nat,X1,sk1_esk64_3(X2,X3,X1)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3070]) ).

cnf(c_0_3070_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X1,X2)),hAPP(nat,nat,X1,X3)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,X1,sk1_esk63_3(X2,X3,X1))),hAPP(nat,nat,X1,sk1_esk64_3(X2,X3,X1)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3070]) ).

cnf(c_0_3070_2,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,X1,sk1_esk63_3(X2,X3,X1))),hAPP(nat,nat,X1,sk1_esk64_3(X2,X3,X1))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X1,X2)),hAPP(nat,nat,X1,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_3070]) ).

cnf(c_0_3071_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X4)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X4))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3071]) ).

cnf(c_0_3071_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X4))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X4)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3071]) ).

cnf(c_0_3071_2,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X4))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_3071]) ).

cnf(c_0_3072_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X4)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X4))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3072]) ).

cnf(c_0_3072_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X4))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X4)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3072]) ).

cnf(c_0_3072_2,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X4))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_3072]) ).

cnf(c_0_3073_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(bool,bool),fun(fun(X1,bool),fun(X1,bool)),combb(bool,bool,X1),fNot),X2))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3073]) ).

cnf(c_0_3073_1,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2)))
    | hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(bool,bool),fun(fun(X1,bool),fun(X1,bool)),combb(bool,bool,X1),fNot),X2))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3073]) ).

cnf(c_0_3073_2,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2)))
    | hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(bool,bool),fun(fun(X1,bool),fun(X1,bool)),combb(bool,bool,X1),fNot),X2)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3073]) ).

cnf(c_0_3076_0,axiom,
    ( hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),hAPP(fun(X1,X2),fun(X2,X1),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)),hilbert_inv_into(X1,X2),top_top(fun(X1,bool))),X3)),X4)) = ti(fun(X2,bool),X4)
    | hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),top_top(fun(X1,bool))) != top_top(fun(X2,bool)) ),
    inference(literals_permutation,[status(thm)],[c_0_3076]) ).

cnf(c_0_3076_1,axiom,
    ( hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),top_top(fun(X1,bool))) != top_top(fun(X2,bool))
    | hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),hAPP(fun(X1,X2),fun(X2,X1),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)),hilbert_inv_into(X1,X2),top_top(fun(X1,bool))),X3)),X4)) = ti(fun(X2,bool),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_3076]) ).

cnf(c_0_3077_0,axiom,
    ( hAPP(X1,X2,X3,hAPP(X2,X1,hAPP(fun(X1,X2),fun(X2,X1),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)),hilbert_inv_into(X1,X2),X4),X3),X5)) = ti(X2,X5)
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X5),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_3077]) ).

cnf(c_0_3077_1,axiom,
    ( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X5),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X4)))
    | hAPP(X1,X2,X3,hAPP(X2,X1,hAPP(fun(X1,X2),fun(X2,X1),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)),hilbert_inv_into(X1,X2),X4),X3),X5)) = ti(X2,X5) ),
    inference(literals_permutation,[status(thm)],[c_0_3077]) ).

cnf(c_0_3078_0,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_3078]) ).

cnf(c_0_3078_1,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_3078]) ).

cnf(c_0_3078_2,axiom,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1)))
    | hAPP(arrow_660593299e_indi,nat,h,X1) != n ),
    inference(literals_permutation,[status(thm)],[c_0_3078]) ).

cnf(c_0_3078_3,axiom,
    ( hAPP(arrow_660593299e_indi,nat,h,X1) != n
    | hAPP(arrow_660593299e_indi,nat,h,X1) = n
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(arrow_660593299e_indi,nat,h,X1)),n))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_3078]) ).

cnf(c_0_3079_0,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X3),X4)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X2) != ti(arrow_490897120le_alt,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_3079]) ).

cnf(c_0_3079_1,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X3),X4)))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X2) != ti(arrow_490897120le_alt,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_3079]) ).

cnf(c_0_3079_2,axiom,
    ( ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X3),X4)))
    | ti(arrow_490897120le_alt,X2) != ti(arrow_490897120le_alt,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_3079]) ).

cnf(c_0_3079_3,axiom,
    ( ti(arrow_490897120le_alt,X2) != ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X3),X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_3079]) ).

cnf(c_0_3080_0,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X3),X4)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X2) != ti(arrow_490897120le_alt,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_3080]) ).

cnf(c_0_3080_1,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X3),X4)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X2) != ti(arrow_490897120le_alt,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_3080]) ).

cnf(c_0_3080_2,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X3),X4)))
    | ti(arrow_490897120le_alt,X2) != ti(arrow_490897120le_alt,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_3080]) ).

cnf(c_0_3080_3,axiom,
    ( ti(arrow_490897120le_alt,X2) != ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1427655034_mktop,X3),X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_3080]) ).

cnf(c_0_3081_0,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X3),X4)))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) != ti(arrow_490897120le_alt,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_3081]) ).

cnf(c_0_3081_1,axiom,
    ( ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X4)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X3),X4)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) != ti(arrow_490897120le_alt,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_3081]) ).

cnf(c_0_3081_2,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X4)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X3),X4)))
    | ti(arrow_490897120le_alt,X1) != ti(arrow_490897120le_alt,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_3081]) ).

cnf(c_0_3081_3,axiom,
    ( ti(arrow_490897120le_alt,X1) != ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X4)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X3),X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_3081]) ).

cnf(c_0_3082_0,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X3),X4)))
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X1) != ti(arrow_490897120le_alt,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_3082]) ).

cnf(c_0_3082_1,axiom,
    ( ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X4)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X3),X4)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X1) != ti(arrow_490897120le_alt,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_3082]) ).

cnf(c_0_3082_2,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X4)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X3),X4)))
    | ti(arrow_490897120le_alt,X1) != ti(arrow_490897120le_alt,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_3082]) ).

cnf(c_0_3082_3,axiom,
    ( ti(arrow_490897120le_alt,X1) != ti(arrow_490897120le_alt,X4)
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | ti(arrow_490897120le_alt,X2) = ti(arrow_490897120le_alt,X4)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),hAPP(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1278947948_mkbot,X3),X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_3082]) ).

cnf(c_0_3083_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
    | ~ linordered_idom(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)),zero_zero(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_3083]) ).

cnf(c_0_3083_1,axiom,
    ( ~ linordered_idom(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)),zero_zero(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_3083]) ).

cnf(c_0_3083_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)),zero_zero(X1)))
    | ~ linordered_idom(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_3083]) ).

cnf(c_0_3084_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
    | ~ linord219039673up_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)),zero_zero(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_3084]) ).

cnf(c_0_3084_1,axiom,
    ( ~ linord219039673up_add(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)),zero_zero(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_3084]) ).

cnf(c_0_3084_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)),zero_zero(X1)))
    | ~ linord219039673up_add(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_3084]) ).

cnf(c_0_3085_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1)))
    | ~ linord219039673up_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)),zero_zero(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_3085]) ).

cnf(c_0_3085_1,axiom,
    ( ~ linord219039673up_add(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)),zero_zero(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_3085]) ).

cnf(c_0_3085_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)),zero_zero(X1)))
    | ~ linord219039673up_add(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_3085]) ).

cnf(c_0_3086_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),ring_1_Ints(X1)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),ring_1_Ints(X1)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),ring_1_Ints(X1)))
    | ~ ring_1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3086]) ).

cnf(c_0_3086_1,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),ring_1_Ints(X1)))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),ring_1_Ints(X1)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),ring_1_Ints(X1)))
    | ~ ring_1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3086]) ).

cnf(c_0_3086_2,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),ring_1_Ints(X1)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),ring_1_Ints(X1)))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),ring_1_Ints(X1)))
    | ~ ring_1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3086]) ).

cnf(c_0_3086_3,axiom,
    ( ~ ring_1(X1)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),ring_1_Ints(X1)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),ring_1_Ints(X1)))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),ring_1_Ints(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_3086]) ).

cnf(c_0_3087_0,axiom,
    ( hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),sk1_esk102_5(X1,X3,X2,X4,X5)) = ti(fun(X1,bool),X2)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_3087]) ).

cnf(c_0_3087_1,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5)))
    | hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),sk1_esk102_5(X1,X3,X2,X4,X5)) = ti(fun(X1,bool),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3087]) ).

cnf(c_0_3088_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X2)),hAPP(fun(X1,bool),nat,finite_card(X1),X3)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3088]) ).

cnf(c_0_3088_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X2)),hAPP(fun(X1,bool),nat,finite_card(X1),X3)))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3088]) ).

cnf(c_0_3088_2,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X2)),hAPP(fun(X1,bool),nat,finite_card(X1),X3)))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3088]) ).

cnf(c_0_3088_3,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X2)),hAPP(fun(X1,bool),nat,finite_card(X1),X3)))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3088]) ).

cnf(c_0_3089_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X3)),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3089]) ).

cnf(c_0_3089_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X3)),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3089]) ).

cnf(c_0_3090_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X1)),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3090]) ).

cnf(c_0_3090_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X1)),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3090]) ).

cnf(c_0_3091_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X3)),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3091]) ).

cnf(c_0_3091_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X3)),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3091]) ).

cnf(c_0_3092_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3092]) ).

cnf(c_0_3092_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),X3))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3092]) ).

cnf(c_0_3093_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3093]) ).

cnf(c_0_3093_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),X3))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3093]) ).

cnf(c_0_3094_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)))
    | ~ ordere236663937imp_le(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3094]) ).

cnf(c_0_3094_1,axiom,
    ( ~ ordere236663937imp_le(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3094]) ).

cnf(c_0_3094_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | ~ ordere236663937imp_le(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_3094]) ).

cnf(c_0_3095_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)))
    | ~ ordere236663937imp_le(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3095]) ).

cnf(c_0_3095_1,axiom,
    ( ~ ordere236663937imp_le(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3095]) ).

cnf(c_0_3095_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
    | ~ ordere236663937imp_le(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_3095]) ).

cnf(c_0_3096_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | ~ ordere223160158up_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3096]) ).

cnf(c_0_3096_1,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)))
    | ~ ordere223160158up_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3096]) ).

cnf(c_0_3096_2,axiom,
    ( ~ ordere223160158up_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_3096]) ).

cnf(c_0_3097_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
    | ~ ordere223160158up_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3097]) ).

cnf(c_0_3097_1,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)))
    | ~ ordere223160158up_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3097]) ).

cnf(c_0_3097_2,axiom,
    ( ~ ordere223160158up_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_3097]) ).

cnf(c_0_3098_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)))
    | ~ ordere236663937imp_le(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3098]) ).

cnf(c_0_3098_1,axiom,
    ( ~ ordere236663937imp_le(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3098]) ).

cnf(c_0_3098_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | ~ ordere236663937imp_le(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_3098]) ).

cnf(c_0_3099_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)))
    | ~ ordere236663937imp_le(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3099]) ).

cnf(c_0_3099_1,axiom,
    ( ~ ordere236663937imp_le(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3099]) ).

cnf(c_0_3099_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
    | ~ ordere236663937imp_le(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_3099]) ).

cnf(c_0_3100_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | ~ ordere779506340up_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3100]) ).

cnf(c_0_3100_1,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)))
    | ~ ordere779506340up_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3100]) ).

cnf(c_0_3100_2,axiom,
    ( ~ ordere779506340up_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_3100]) ).

cnf(c_0_3101_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
    | ~ ordere779506340up_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3101]) ).

cnf(c_0_3101_1,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)))
    | ~ ordere779506340up_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3101]) ).

cnf(c_0_3101_2,axiom,
    ( ~ ordere779506340up_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_3101]) ).

cnf(c_0_3102_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X4),X5))
    | hAPP(X1,X2,X3,sk1_esk71_5(X2,X1,X3,X4,X5)) != hAPP(X1,X2,X4,sk1_esk71_5(X2,X1,X3,X4,X5))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_3102]) ).

cnf(c_0_3102_1,axiom,
    ( hAPP(X1,X2,X3,sk1_esk71_5(X2,X1,X3,X4,X5)) != hAPP(X1,X2,X4,sk1_esk71_5(X2,X1,X3,X4,X5))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X4),X5))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_3102]) ).

cnf(c_0_3102_2,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X5))
    | hAPP(X1,X2,X3,sk1_esk71_5(X2,X1,X3,X4,X5)) != hAPP(X1,X2,X4,sk1_esk71_5(X2,X1,X3,X4,X5))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X4),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_3102]) ).

cnf(c_0_3103_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X5))
    | hAPP(X1,X2,X3,sk1_esk71_5(X2,X1,X3,X4,X5)) != hAPP(X1,X2,X4,sk1_esk71_5(X2,X1,X3,X4,X5))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X4),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_3103]) ).

cnf(c_0_3103_1,axiom,
    ( hAPP(X1,X2,X3,sk1_esk71_5(X2,X1,X3,X4,X5)) != hAPP(X1,X2,X4,sk1_esk71_5(X2,X1,X3,X4,X5))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X5))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X4),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_3103]) ).

cnf(c_0_3103_2,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X4),X5))
    | hAPP(X1,X2,X3,sk1_esk71_5(X2,X1,X3,X4,X5)) != hAPP(X1,X2,X4,sk1_esk71_5(X2,X1,X3,X4,X5))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_3103]) ).

cnf(c_0_3104_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3104]) ).

cnf(c_0_3104_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_3104]) ).

cnf(c_0_3105_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X3)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3105]) ).

cnf(c_0_3105_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_3105]) ).

cnf(c_0_3106_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3106]) ).

cnf(c_0_3106_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X3))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_3106]) ).

cnf(c_0_3107_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X3)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3107]) ).

cnf(c_0_3107_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_3107]) ).

cnf(c_0_3108_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X2),X3)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3108]) ).

cnf(c_0_3108_1,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X2),X3)))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3108]) ).

cnf(c_0_3108_2,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X2),X3)))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3108]) ).

cnf(c_0_3109_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),zero_zero(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),zero_zero(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
    | ~ ordere216010020id_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3109]) ).

cnf(c_0_3109_1,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),zero_zero(X1)))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),zero_zero(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
    | ~ ordere216010020id_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3109]) ).

cnf(c_0_3109_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),zero_zero(X1)))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),zero_zero(X1)))
    | ~ ordere216010020id_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3109]) ).

cnf(c_0_3109_3,axiom,
    ( ~ ordere216010020id_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),zero_zero(X1)))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),zero_zero(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_3109]) ).

cnf(c_0_3110_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),zero_zero(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),zero_zero(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1)))
    | ~ ordere216010020id_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3110]) ).

cnf(c_0_3110_1,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),zero_zero(X1)))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),zero_zero(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1)))
    | ~ ordere216010020id_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3110]) ).

cnf(c_0_3110_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),zero_zero(X1)))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),zero_zero(X1)))
    | ~ ordere216010020id_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3110]) ).

cnf(c_0_3110_3,axiom,
    ( ~ ordere216010020id_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),zero_zero(X1)))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),zero_zero(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_3110]) ).

cnf(c_0_3111_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),zero_zero(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),zero_zero(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
    | ~ ordere216010020id_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3111]) ).

cnf(c_0_3111_1,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),zero_zero(X1)))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),zero_zero(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
    | ~ ordere216010020id_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3111]) ).

cnf(c_0_3111_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),zero_zero(X1)))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),zero_zero(X1)))
    | ~ ordere216010020id_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3111]) ).

cnf(c_0_3111_3,axiom,
    ( ~ ordere216010020id_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),zero_zero(X1)))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),zero_zero(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_3111]) ).

cnf(c_0_3112_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),zero_zero(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),zero_zero(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1)))
    | ~ ordere216010020id_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3112]) ).

cnf(c_0_3112_1,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),zero_zero(X1)))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),zero_zero(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1)))
    | ~ ordere216010020id_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3112]) ).

cnf(c_0_3112_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),zero_zero(X1)))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),zero_zero(X1)))
    | ~ ordere216010020id_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3112]) ).

cnf(c_0_3112_3,axiom,
    ( ~ ordere216010020id_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),zero_zero(X1)))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),zero_zero(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_3112]) ).

cnf(c_0_3113_0,axiom,
    ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,X1))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sk1_esk16_1(X1)),sk1_esk17_1(X1))),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),sk1_esk15_1(X1),X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_3113]) ).

cnf(c_0_3113_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),sk1_esk16_1(X1)),sk1_esk17_1(X1))),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),sk1_esk15_1(X1),X2)))
    | hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_3113]) ).

cnf(c_0_3114_0,axiom,
    ( hAPP(X3,X1,X4,sk1_esk101_5(X1,X3,X2,X4,X5)) = ti(X1,X2)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_3114]) ).

cnf(c_0_3114_1,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5)))
    | hAPP(X3,X1,X4,sk1_esk101_5(X1,X3,X2,X4,X5)) = ti(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3114]) ).

cnf(c_0_3118_0,axiom,
    ( hAPP(fun(X1,bool),nat,hAPP(nat,fun(fun(X1,bool),nat),hAPP(fun(X1,nat),fun(nat,fun(fun(X1,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(X1,nat),fun(nat,fun(fun(X1,bool),nat))),finite_fold_image(nat,X1),plus_plus(nat)),hAPP(nat,fun(X1,nat),combk(nat,X1),one_one(nat))),zero_zero(nat)),X2) = hAPP(fun(X1,bool),nat,finite_card(X1),X2)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3118]) ).

cnf(c_0_3118_1,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | hAPP(fun(X1,bool),nat,hAPP(nat,fun(fun(X1,bool),nat),hAPP(fun(X1,nat),fun(nat,fun(fun(X1,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(X1,nat),fun(nat,fun(fun(X1,bool),nat))),finite_fold_image(nat,X1),plus_plus(nat)),hAPP(nat,fun(X1,nat),combk(nat,X1),one_one(nat))),zero_zero(nat)),X2) = hAPP(fun(X1,bool),nat,finite_card(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3118]) ).

cnf(c_0_3119_0,axiom,
    ( hAPP(fun(X1,bool),nat,hAPP(nat,fun(fun(X1,bool),nat),hAPP(fun(X1,nat),fun(nat,fun(fun(X1,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(X1,nat),fun(nat,fun(fun(X1,bool),nat))),finite_fold_image(nat,X1),plus_plus(nat)),hAPP(nat,fun(X1,nat),combk(nat,X1),one_one(nat))),zero_zero(nat)),X2) = hAPP(fun(X1,bool),nat,finite_card(X1),X2)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3119]) ).

cnf(c_0_3119_1,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | hAPP(fun(X1,bool),nat,hAPP(nat,fun(fun(X1,bool),nat),hAPP(fun(X1,nat),fun(nat,fun(fun(X1,bool),nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(X1,nat),fun(nat,fun(fun(X1,bool),nat))),finite_fold_image(nat,X1),plus_plus(nat)),hAPP(nat,fun(X1,nat),combk(nat,X1),one_one(nat))),zero_zero(nat)),X2) = hAPP(fun(X1,bool),nat,finite_card(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3119]) ).

cnf(c_0_3120_0,axiom,
    ( ti(fun(X1,bool),X2) = ti(fun(X1,bool),X3)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X3)),hAPP(fun(X1,bool),nat,finite_card(X1),X2)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3120]) ).

cnf(c_0_3120_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X3)),hAPP(fun(X1,bool),nat,finite_card(X1),X2)))
    | ti(fun(X1,bool),X2) = ti(fun(X1,bool),X3)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3120]) ).

cnf(c_0_3120_2,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X3)),hAPP(fun(X1,bool),nat,finite_card(X1),X2)))
    | ti(fun(X1,bool),X2) = ti(fun(X1,bool),X3)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3120]) ).

cnf(c_0_3120_3,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X3)),hAPP(fun(X1,bool),nat,finite_card(X1),X2)))
    | ti(fun(X1,bool),X2) = ti(fun(X1,bool),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3120]) ).

cnf(c_0_3121_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5)))
    | ti(fun(X1,bool),X2) != hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X6)
    | ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X6),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_3121]) ).

cnf(c_0_3121_1,axiom,
    ( ti(fun(X1,bool),X2) != hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X6)
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5)))
    | ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X6),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_3121]) ).

cnf(c_0_3121_2,axiom,
    ( ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(fun(X3,bool),fun(fun(X3,bool),bool),ord_less_eq(fun(X3,bool)),X6),X5))
    | ti(fun(X1,bool),X2) != hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X6)
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_3121]) ).

cnf(c_0_3125_0,axiom,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X5)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X5))
    | ~ comm_semiring_1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3125]) ).

cnf(c_0_3125_1,axiom,
    ( ~ comm_semiring_1(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X5)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_3125]) ).

cnf(c_0_3126_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X2,X1,X3,X4)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X5)))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X4),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_3126]) ).

cnf(c_0_3126_1,axiom,
    ( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X4),X5))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X2,X1,X3,X4)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_3126]) ).

cnf(c_0_3127_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)),zero_zero(X1)))
    | ~ linordered_idom(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_3127]) ).

cnf(c_0_3127_1,axiom,
    ( ~ linordered_idom(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)),zero_zero(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_3127]) ).

cnf(c_0_3127_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
    | ~ linordered_idom(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)),zero_zero(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_3127]) ).

cnf(c_0_3128_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)),zero_zero(X1)))
    | ~ linord219039673up_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_3128]) ).

cnf(c_0_3128_1,axiom,
    ( ~ linord219039673up_add(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)),zero_zero(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_3128]) ).

cnf(c_0_3128_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),zero_zero(X1)))
    | ~ linord219039673up_add(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)),zero_zero(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_3128]) ).

cnf(c_0_3129_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)),zero_zero(X1)))
    | ~ linord219039673up_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_3129]) ).

cnf(c_0_3129_1,axiom,
    ( ~ linord219039673up_add(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)),zero_zero(X1)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_3129]) ).

cnf(c_0_3129_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),zero_zero(X1)))
    | ~ linord219039673up_add(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)),zero_zero(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_3129]) ).

cnf(c_0_3130_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_3130]) ).

cnf(c_0_3130_1,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_3130]) ).

cnf(c_0_3130_2,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X1)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_3130]) ).

cnf(c_0_3131_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ hBOOL(hAPP(fun(sum_sum(X3,X1),bool),bool,finite_finite_1(sum_sum(X3,X1)),hAPP(fun(X1,bool),fun(sum_sum(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X1,bool),fun(sum_sum(X3,X1),bool)),sum_Plus(X3,X1),X4),X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_3131]) ).

cnf(c_0_3131_1,axiom,
    ( ~ hBOOL(hAPP(fun(sum_sum(X3,X1),bool),bool,finite_finite_1(sum_sum(X3,X1)),hAPP(fun(X1,bool),fun(sum_sum(X3,X1),bool),hAPP(fun(X3,bool),fun(fun(X1,bool),fun(sum_sum(X3,X1),bool)),sum_Plus(X3,X1),X4),X2)))
    | hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3131]) ).

cnf(c_0_3132_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ hBOOL(hAPP(fun(sum_sum(X1,X3),bool),bool,finite_finite_1(sum_sum(X1,X3)),hAPP(fun(X3,bool),fun(sum_sum(X1,X3),bool),hAPP(fun(X1,bool),fun(fun(X3,bool),fun(sum_sum(X1,X3),bool)),sum_Plus(X1,X3),X2),X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_3132]) ).

cnf(c_0_3132_1,axiom,
    ( ~ hBOOL(hAPP(fun(sum_sum(X1,X3),bool),bool,finite_finite_1(sum_sum(X1,X3)),hAPP(fun(X3,bool),fun(sum_sum(X1,X3),bool),hAPP(fun(X1,bool),fun(fun(X3,bool),fun(sum_sum(X1,X3),bool)),sum_Plus(X1,X3),X2),X4)))
    | hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3132]) ).

cnf(c_0_3133_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3))
    | ~ hBOOL(hAPP(fun(sum_sum(X1,X2),bool),bool,finite_finite_1(sum_sum(X1,X2)),hAPP(fun(X2,bool),fun(sum_sum(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X2,bool),fun(sum_sum(X1,X2),bool)),sum_Plus(X1,X2),X3),X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_3133]) ).

cnf(c_0_3133_1,axiom,
    ( ~ hBOOL(hAPP(fun(sum_sum(X1,X2),bool),bool,finite_finite_1(sum_sum(X1,X2)),hAPP(fun(X2,bool),fun(sum_sum(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X2,bool),fun(sum_sum(X1,X2),bool)),sum_Plus(X1,X2),X3),X4)))
    | hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3133]) ).

cnf(c_0_3134_0,axiom,
    ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
    | ~ hBOOL(hAPP(fun(sum_sum(X1,X2),bool),bool,finite_finite_1(sum_sum(X1,X2)),hAPP(fun(X2,bool),fun(sum_sum(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X2,bool),fun(sum_sum(X1,X2),bool)),sum_Plus(X1,X2),X3),X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_3134]) ).

cnf(c_0_3134_1,axiom,
    ( ~ hBOOL(hAPP(fun(sum_sum(X1,X2),bool),bool,finite_finite_1(sum_sum(X1,X2)),hAPP(fun(X2,bool),fun(sum_sum(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X2,bool),fun(sum_sum(X1,X2),bool)),sum_Plus(X1,X2),X3),X4)))
    | hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3134]) ).

cnf(c_0_3135_0,axiom,
    ( hBOOL(hAPP(fun(X1,fun(X2,bool)),bool,hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,fun(X2,bool)),bool),ord_less_eq(fun(X1,fun(X2,bool))),X3),X4))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X4,sk1_esk50_4(X2,X1,X4,X3)),sk1_esk51_4(X2,X1,X4,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_3135]) ).

cnf(c_0_3135_1,axiom,
    ( ~ hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X4,sk1_esk50_4(X2,X1,X4,X3)),sk1_esk51_4(X2,X1,X4,X3)))
    | hBOOL(hAPP(fun(X1,fun(X2,bool)),bool,hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,fun(X2,bool)),bool),ord_less_eq(fun(X1,fun(X2,bool))),X3),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3135]) ).

cnf(c_0_3136_0,axiom,
    ( hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,X1),X2))
    | hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),sk1_esk32_2(X1,X2)),arrow_1111136790e_Prof)) ),
    inference(literals_permutation,[status(thm)],[c_0_3136]) ).

cnf(c_0_3136_1,axiom,
    ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),sk1_esk32_2(X1,X2)),arrow_1111136790e_Prof))
    | hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3136]) ).

cnf(c_0_3137_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
    | ~ ordere216010020id_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3137]) ).

cnf(c_0_3137_1,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
    | ~ ordere216010020id_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3137]) ).

cnf(c_0_3137_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)))
    | ~ ordere216010020id_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3137]) ).

cnf(c_0_3137_3,axiom,
    ( ~ ordere216010020id_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_3137]) ).

cnf(c_0_3138_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
    | ~ ordere216010020id_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3138]) ).

cnf(c_0_3138_1,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
    | ~ ordere216010020id_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3138]) ).

cnf(c_0_3138_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)))
    | ~ ordere216010020id_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3138]) ).

cnf(c_0_3138_3,axiom,
    ( ~ ordere216010020id_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_3138]) ).

cnf(c_0_3139_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
    | ~ ordere216010020id_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3139]) ).

cnf(c_0_3139_1,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
    | ~ ordere216010020id_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3139]) ).

cnf(c_0_3139_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)))
    | ~ ordere216010020id_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3139]) ).

cnf(c_0_3139_3,axiom,
    ( ~ ordere216010020id_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_3139]) ).

cnf(c_0_3140_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
    | ~ ordere216010020id_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3140]) ).

cnf(c_0_3140_1,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
    | ~ ordere216010020id_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3140]) ).

cnf(c_0_3140_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)))
    | ~ ordere216010020id_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3140]) ).

cnf(c_0_3140_3,axiom,
    ( ~ ordere216010020id_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_3140]) ).

cnf(c_0_3142_0,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),sk1_esk26_2(X1,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_3142]) ).

cnf(c_0_3142_1,axiom,
    ( hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),X1),X2)),sk1_esk26_2(X1,X2)))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3142]) ).

cnf(c_0_3143_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
    | ~ ordere216010020id_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3143]) ).

cnf(c_0_3143_1,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
    | ~ ordere216010020id_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3143]) ).

cnf(c_0_3143_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)))
    | ~ ordere216010020id_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3143]) ).

cnf(c_0_3143_3,axiom,
    ( ~ ordere216010020id_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_3143]) ).

cnf(c_0_3144_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
    | ~ ordere216010020id_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3144]) ).

cnf(c_0_3144_1,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
    | ~ ordere216010020id_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3144]) ).

cnf(c_0_3144_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)))
    | ~ ordere216010020id_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3144]) ).

cnf(c_0_3144_3,axiom,
    ( ~ ordere216010020id_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_3144]) ).

cnf(c_0_3145_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
    | ~ linordered_semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3145]) ).

cnf(c_0_3145_1,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
    | ~ linordered_semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3145]) ).

cnf(c_0_3145_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)))
    | ~ linordered_semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3145]) ).

cnf(c_0_3145_3,axiom,
    ( ~ linordered_semidom(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_3145]) ).

cnf(c_0_3146_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
    | ~ ordere216010020id_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3146]) ).

cnf(c_0_3146_1,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
    | ~ ordere216010020id_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3146]) ).

cnf(c_0_3146_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)))
    | ~ ordere216010020id_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3146]) ).

cnf(c_0_3146_3,axiom,
    ( ~ ordere216010020id_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_3146]) ).

cnf(c_0_3147_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X4))
    | ~ ordere216010020id_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3147]) ).

cnf(c_0_3147_1,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X4))
    | ~ ordere216010020id_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3147]) ).

cnf(c_0_3147_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)))
    | ~ ordere216010020id_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3147]) ).

cnf(c_0_3147_3,axiom,
    ( ~ ordere216010020id_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_3147]) ).

cnf(c_0_3148_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ linordered_field(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),sk1_esk99_3(X1,X2,X3)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3148]) ).

cnf(c_0_3148_1,axiom,
    ( ~ linordered_field(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),sk1_esk99_3(X1,X2,X3)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3148]) ).

cnf(c_0_3148_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),sk1_esk99_3(X1,X2,X3))))
    | ~ linordered_field(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3148]) ).

cnf(c_0_3154_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
    | ~ dense_linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),sk1_esk38_4(X1,X4,X2,X3)),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3154]) ).

cnf(c_0_3154_1,axiom,
    ( ~ dense_linorder(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),sk1_esk38_4(X1,X4,X2,X3)),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3154]) ).

cnf(c_0_3154_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ dense_linorder(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),sk1_esk38_4(X1,X4,X2,X3)),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3154]) ).

cnf(c_0_3154_3,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),sk1_esk38_4(X1,X4,X2,X3)),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ dense_linorder(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3154]) ).

cnf(c_0_3155_0,axiom,
    ( ti(X1,X2) = ti(X1,X3)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
    | hAPP(X1,X5,X6,X2) != hAPP(X1,X5,X6,X3)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X5),fun(fun(X1,bool),bool),inj_on(X1,X5),X6),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3155]) ).

cnf(c_0_3155_1,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X4))
    | ti(X1,X2) = ti(X1,X3)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
    | hAPP(X1,X5,X6,X2) != hAPP(X1,X5,X6,X3)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X5),fun(fun(X1,bool),bool),inj_on(X1,X5),X6),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3155]) ).

cnf(c_0_3155_2,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X4))
    | ti(X1,X2) = ti(X1,X3)
    | hAPP(X1,X5,X6,X2) != hAPP(X1,X5,X6,X3)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X5),fun(fun(X1,bool),bool),inj_on(X1,X5),X6),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3155]) ).

cnf(c_0_3155_3,axiom,
    ( hAPP(X1,X5,X6,X2) != hAPP(X1,X5,X6,X3)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X4))
    | ti(X1,X2) = ti(X1,X3)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X5),fun(fun(X1,bool),bool),inj_on(X1,X5),X6),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3155]) ).

cnf(c_0_3155_4,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X5),fun(fun(X1,bool),bool),inj_on(X1,X5),X6),X4))
    | hAPP(X1,X5,X6,X2) != hAPP(X1,X5,X6,X3)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X4))
    | ti(X1,X2) = ti(X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3155]) ).

cnf(c_0_3156_0,axiom,
    ( ti(X1,X5) = ti(X1,X6)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X4))
    | hAPP(X1,X2,X3,X5) != hAPP(X1,X2,X3,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_3156]) ).

cnf(c_0_3156_1,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | ti(X1,X5) = ti(X1,X6)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X4))
    | hAPP(X1,X2,X3,X5) != hAPP(X1,X2,X3,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_3156]) ).

cnf(c_0_3156_2,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | ti(X1,X5) = ti(X1,X6)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X4))
    | hAPP(X1,X2,X3,X5) != hAPP(X1,X2,X3,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_3156]) ).

cnf(c_0_3156_3,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | ti(X1,X5) = ti(X1,X6)
    | hAPP(X1,X2,X3,X5) != hAPP(X1,X2,X3,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_3156]) ).

cnf(c_0_3156_4,axiom,
    ( hAPP(X1,X2,X3,X5) != hAPP(X1,X2,X3,X6)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | ti(X1,X5) = ti(X1,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_3156]) ).

cnf(c_0_3157_0,axiom,
    ( ti(X1,X4) = ti(X1,X5)
    | hAPP(X1,X2,X3,X4) != hAPP(X1,X2,X3,X5)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X6))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X6))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_3157]) ).

cnf(c_0_3157_1,axiom,
    ( hAPP(X1,X2,X3,X4) != hAPP(X1,X2,X3,X5)
    | ti(X1,X4) = ti(X1,X5)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X6))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X6))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_3157]) ).

cnf(c_0_3157_2,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X6))
    | hAPP(X1,X2,X3,X4) != hAPP(X1,X2,X3,X5)
    | ti(X1,X4) = ti(X1,X5)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X6))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_3157]) ).

cnf(c_0_3157_3,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X6))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X6))
    | hAPP(X1,X2,X3,X4) != hAPP(X1,X2,X3,X5)
    | ti(X1,X4) = ti(X1,X5)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_3157]) ).

cnf(c_0_3157_4,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X6))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X4),X6))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X6))
    | hAPP(X1,X2,X3,X4) != hAPP(X1,X2,X3,X5)
    | ti(X1,X4) = ti(X1,X5) ),
    inference(literals_permutation,[status(thm)],[c_0_3157]) ).

cnf(c_0_3158_0,axiom,
    ( ti(X1,X2) = ti(X1,X3)
    | hAPP(X1,X4,X5,X2) != hAPP(X1,X4,X5,X3)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X6))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X6))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X4),fun(fun(X1,bool),bool),inj_on(X1,X4),X5),X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_3158]) ).

cnf(c_0_3158_1,axiom,
    ( hAPP(X1,X4,X5,X2) != hAPP(X1,X4,X5,X3)
    | ti(X1,X2) = ti(X1,X3)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X6))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X6))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X4),fun(fun(X1,bool),bool),inj_on(X1,X4),X5),X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_3158]) ).

cnf(c_0_3158_2,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X6))
    | hAPP(X1,X4,X5,X2) != hAPP(X1,X4,X5,X3)
    | ti(X1,X2) = ti(X1,X3)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X6))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X4),fun(fun(X1,bool),bool),inj_on(X1,X4),X5),X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_3158]) ).

cnf(c_0_3158_3,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X6))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X6))
    | hAPP(X1,X4,X5,X2) != hAPP(X1,X4,X5,X3)
    | ti(X1,X2) = ti(X1,X3)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X4),fun(fun(X1,bool),bool),inj_on(X1,X4),X5),X6)) ),
    inference(literals_permutation,[status(thm)],[c_0_3158]) ).

cnf(c_0_3158_4,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X4),fun(fun(X1,bool),bool),inj_on(X1,X4),X5),X6))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X6))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X6))
    | hAPP(X1,X4,X5,X2) != hAPP(X1,X4,X5,X3)
    | ti(X1,X2) = ti(X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3158]) ).

cnf(c_0_3159_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5)))
    | ti(X1,X2) != hAPP(X3,X1,X4,X6)
    | ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_3159]) ).

cnf(c_0_3159_1,axiom,
    ( ti(X1,X2) != hAPP(X3,X1,X4,X6)
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5)))
    | ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_3159]) ).

cnf(c_0_3159_2,axiom,
    ( ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X5))
    | ti(X1,X2) != hAPP(X3,X1,X4,X6)
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_3159]) ).

cnf(c_0_3160_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5)))
    | ti(X1,X2) != hAPP(X3,X1,X4,X6)
    | ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_3160]) ).

cnf(c_0_3160_1,axiom,
    ( ti(X1,X2) != hAPP(X3,X1,X4,X6)
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5)))
    | ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_3160]) ).

cnf(c_0_3160_2,axiom,
    ( ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X5))
    | ti(X1,X2) != hAPP(X3,X1,X4,X6)
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_3160]) ).

cnf(c_0_3161_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5)))
    | ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X5))
    | ti(X1,X2) != hAPP(X3,X1,X4,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_3161]) ).

cnf(c_0_3161_1,axiom,
    ( ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X5))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5)))
    | ti(X1,X2) != hAPP(X3,X1,X4,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_3161]) ).

cnf(c_0_3161_2,axiom,
    ( ti(X1,X2) != hAPP(X3,X1,X4,X6)
    | ~ hBOOL(hAPP(fun(X3,bool),bool,hAPP(X3,fun(fun(X3,bool),bool),member(X3),X6),X5))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_3161]) ).

cnf(c_0_3162_0,axiom,
    ( hBOOL(hAPP(product_prod(X1,X2),bool,X3,X4))
    | ~ hBOOL(hAPP(product_prod(X1,X2),bool,X3,hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),sk1_esk7_3(X1,X2,X3)),sk1_esk8_3(X1,X2,X3)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3162]) ).

cnf(c_0_3162_1,axiom,
    ( ~ hBOOL(hAPP(product_prod(X1,X2),bool,X3,hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),sk1_esk7_3(X1,X2,X3)),sk1_esk8_3(X1,X2,X3))))
    | hBOOL(hAPP(product_prod(X1,X2),bool,X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3162]) ).

cnf(c_0_3163_0,axiom,
    ( hAPP(X1,X2,X3,X5) = hAPP(X1,X2,X3,X6)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X4))
    | ti(X1,X5) != ti(X1,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_3163]) ).

cnf(c_0_3163_1,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | hAPP(X1,X2,X3,X5) = hAPP(X1,X2,X3,X6)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X4))
    | ti(X1,X5) != ti(X1,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_3163]) ).

cnf(c_0_3163_2,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | hAPP(X1,X2,X3,X5) = hAPP(X1,X2,X3,X6)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X4))
    | ti(X1,X5) != ti(X1,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_3163]) ).

cnf(c_0_3163_3,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | hAPP(X1,X2,X3,X5) = hAPP(X1,X2,X3,X6)
    | ti(X1,X5) != ti(X1,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_3163]) ).

cnf(c_0_3163_4,axiom,
    ( ti(X1,X5) != ti(X1,X6)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X6),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X5),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | hAPP(X1,X2,X3,X5) = hAPP(X1,X2,X3,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_3163]) ).

cnf(c_0_3164_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
    | ~ linord219039673up_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_3164]) ).

cnf(c_0_3164_1,axiom,
    ( ~ linord219039673up_add(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_3164]) ).

cnf(c_0_3164_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)))
    | ~ linord219039673up_add(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3164]) ).

cnf(c_0_3165_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
    | ~ linord219039673up_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_3165]) ).

cnf(c_0_3165_1,axiom,
    ( ~ linord219039673up_add(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_3165]) ).

cnf(c_0_3165_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)))
    | ~ linord219039673up_add(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3165]) ).

cnf(c_0_3166_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X1,X2)),hAPP(nat,nat,X1,X3)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sk1_esk63_3(X2,X3,X1)),sk1_esk64_3(X2,X3,X1)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3166]) ).

cnf(c_0_3166_1,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sk1_esk63_3(X2,X3,X1)),sk1_esk64_3(X2,X3,X1)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X1,X2)),hAPP(nat,nat,X1,X3)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3166]) ).

cnf(c_0_3166_2,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X3))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sk1_esk63_3(X2,X3,X1)),sk1_esk64_3(X2,X3,X1)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,X1,X2)),hAPP(nat,nat,X1,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_3166]) ).

cnf(c_0_3167_0,axiom,
    ( hAPP(X1,X2,hAPP(fun(X2,X1),fun(X1,X2),hAPP(fun(X2,bool),fun(fun(X2,X1),fun(X1,X2)),hilbert_inv_into(X2,X1),X3),X4),hAPP(X2,X1,X4,X5)) = ti(X2,X5)
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X5),X3))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),inj_on(X2,X1),X4),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3167]) ).

cnf(c_0_3167_1,axiom,
    ( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X5),X3))
    | hAPP(X1,X2,hAPP(fun(X2,X1),fun(X1,X2),hAPP(fun(X2,bool),fun(fun(X2,X1),fun(X1,X2)),hilbert_inv_into(X2,X1),X3),X4),hAPP(X2,X1,X4,X5)) = ti(X2,X5)
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),inj_on(X2,X1),X4),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3167]) ).

cnf(c_0_3167_2,axiom,
    ( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),inj_on(X2,X1),X4),X3))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X5),X3))
    | hAPP(X1,X2,hAPP(fun(X2,X1),fun(X1,X2),hAPP(fun(X2,bool),fun(fun(X2,X1),fun(X1,X2)),hilbert_inv_into(X2,X1),X3),X4),hAPP(X2,X1,X4,X5)) = ti(X2,X5) ),
    inference(literals_permutation,[status(thm)],[c_0_3167]) ).

cnf(c_0_3168_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X3,X4),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X6,X4),X5))
    | ~ hBOOL(hAPP(fun(X2,fun(X1,bool)),bool,hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),bool),ord_less_eq(fun(X2,fun(X1,bool))),X6),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3168]) ).

cnf(c_0_3168_1,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X6,X4),X5))
    | hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X3,X4),X5))
    | ~ hBOOL(hAPP(fun(X2,fun(X1,bool)),bool,hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),bool),ord_less_eq(fun(X2,fun(X1,bool))),X6),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3168]) ).

cnf(c_0_3168_2,axiom,
    ( ~ hBOOL(hAPP(fun(X2,fun(X1,bool)),bool,hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),bool),ord_less_eq(fun(X2,fun(X1,bool))),X6),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X6,X4),X5))
    | hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X3,X4),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_3168]) ).

cnf(c_0_3169_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X3,X4),X5))
    | ~ hBOOL(hAPP(fun(X2,fun(X1,bool)),bool,hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),bool),ord_less_eq(fun(X2,fun(X1,bool))),X6),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X6,X4),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_3169]) ).

cnf(c_0_3169_1,axiom,
    ( ~ hBOOL(hAPP(fun(X2,fun(X1,bool)),bool,hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),bool),ord_less_eq(fun(X2,fun(X1,bool))),X6),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X3,X4),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X6,X4),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_3169]) ).

cnf(c_0_3169_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X6,X4),X5))
    | ~ hBOOL(hAPP(fun(X2,fun(X1,bool)),bool,hAPP(fun(X2,fun(X1,bool)),fun(fun(X2,fun(X1,bool)),bool),ord_less_eq(fun(X2,fun(X1,bool))),X6),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X2,fun(X1,bool),X3,X4),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_3169]) ).

cnf(c_0_3170_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X2)),hAPP(fun(X1,bool),nat,finite_card(X1),X3)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3170]) ).

cnf(c_0_3170_1,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X2)),hAPP(fun(X1,bool),nat,finite_card(X1),X3)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3170]) ).

cnf(c_0_3170_2,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X2)),hAPP(fun(X1,bool),nat,finite_card(X1),X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_3170]) ).

cnf(c_0_3171_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X2)),hAPP(fun(X1,bool),nat,finite_card(X1),X3)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3171]) ).

cnf(c_0_3171_1,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X2)),hAPP(fun(X1,bool),nat,finite_card(X1),X3)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3171]) ).

cnf(c_0_3171_2,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X2)),hAPP(fun(X1,bool),nat,finite_card(X1),X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_3171]) ).

cnf(c_0_3172_0,axiom,
    ( hAPP(X1,X2,hAPP(fun(X2,X1),fun(X1,X2),hAPP(fun(X2,bool),fun(fun(X2,X1),fun(X1,X2)),hilbert_inv_into(X2,X1),X3),X4),X5) = ti(X2,X6)
    | hAPP(X2,X1,X4,X6) != ti(X1,X5)
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X6),X3))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),inj_on(X2,X1),X4),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3172]) ).

cnf(c_0_3172_1,axiom,
    ( hAPP(X2,X1,X4,X6) != ti(X1,X5)
    | hAPP(X1,X2,hAPP(fun(X2,X1),fun(X1,X2),hAPP(fun(X2,bool),fun(fun(X2,X1),fun(X1,X2)),hilbert_inv_into(X2,X1),X3),X4),X5) = ti(X2,X6)
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X6),X3))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),inj_on(X2,X1),X4),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3172]) ).

cnf(c_0_3172_2,axiom,
    ( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X6),X3))
    | hAPP(X2,X1,X4,X6) != ti(X1,X5)
    | hAPP(X1,X2,hAPP(fun(X2,X1),fun(X1,X2),hAPP(fun(X2,bool),fun(fun(X2,X1),fun(X1,X2)),hilbert_inv_into(X2,X1),X3),X4),X5) = ti(X2,X6)
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),inj_on(X2,X1),X4),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3172]) ).

cnf(c_0_3172_3,axiom,
    ( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),inj_on(X2,X1),X4),X3))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(X2,fun(fun(X2,bool),bool),member(X2),X6),X3))
    | hAPP(X2,X1,X4,X6) != ti(X1,X5)
    | hAPP(X1,X2,hAPP(fun(X2,X1),fun(X1,X2),hAPP(fun(X2,bool),fun(fun(X2,X1),fun(X1,X2)),hilbert_inv_into(X2,X1),X3),X4),X5) = ti(X2,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_3172]) ).

cnf(c_0_3173_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3173]) ).

cnf(c_0_3173_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3173]) ).

cnf(c_0_3173_2,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3173]) ).

cnf(c_0_3173_3,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3173]) ).

cnf(c_0_3176_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X4),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3176]) ).

cnf(c_0_3176_1,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X4),X3))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3176]) ).

cnf(c_0_3176_2,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X4),X3))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3176]) ).

cnf(c_0_3177_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3177]) ).

cnf(c_0_3177_1,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3177]) ).

cnf(c_0_3177_2,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3177]) ).

cnf(c_0_3178_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X4),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3178]) ).

cnf(c_0_3178_1,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X4),X3))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3178]) ).

cnf(c_0_3178_2,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X4),X3))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3178]) ).

cnf(c_0_3179_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3179]) ).

cnf(c_0_3179_1,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3179]) ).

cnf(c_0_3179_2,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3179]) ).

cnf(c_0_3180_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),hAPP(nat,nat,suc,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_3180]) ).

cnf(c_0_3180_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),hAPP(nat,nat,suc,X2)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3180]) ).

cnf(c_0_3181_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),hAPP(nat,nat,suc,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_3181]) ).

cnf(c_0_3181_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),hAPP(nat,nat,suc,X2)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3181]) ).

cnf(c_0_3182_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),hAPP(nat,nat,suc,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_3182]) ).

cnf(c_0_3182_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),hAPP(nat,nat,suc,X2)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3182]) ).

cnf(c_0_3184_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X5))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_3184]) ).

cnf(c_0_3184_1,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X5))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_3184]) ).

cnf(c_0_3184_2,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X5))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X5))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3184]) ).

cnf(c_0_3185_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3185]) ).

cnf(c_0_3185_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3185]) ).

cnf(c_0_3185_2,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3185]) ).

cnf(c_0_3186_0,axiom,
    ( hAPP(fun(X1,X2),fun(X2,X1),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)),hilbert_inv_into(X1,X2),top_top(fun(X1,bool))),X3) = ti(fun(X2,X1),X4)
    | hAPP(X1,X2,X3,hAPP(X2,X1,X4,sk1_esk34_4(X1,X2,X4,X3))) != ti(X2,sk1_esk34_4(X1,X2,X4,X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),top_top(fun(X1,bool)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3186]) ).

cnf(c_0_3186_1,axiom,
    ( hAPP(X1,X2,X3,hAPP(X2,X1,X4,sk1_esk34_4(X1,X2,X4,X3))) != ti(X2,sk1_esk34_4(X1,X2,X4,X3))
    | hAPP(fun(X1,X2),fun(X2,X1),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)),hilbert_inv_into(X1,X2),top_top(fun(X1,bool))),X3) = ti(fun(X2,X1),X4)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),top_top(fun(X1,bool)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3186]) ).

cnf(c_0_3186_2,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),top_top(fun(X1,bool))))
    | hAPP(X1,X2,X3,hAPP(X2,X1,X4,sk1_esk34_4(X1,X2,X4,X3))) != ti(X2,sk1_esk34_4(X1,X2,X4,X3))
    | hAPP(fun(X1,X2),fun(X2,X1),hAPP(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1)),hilbert_inv_into(X1,X2),top_top(fun(X1,bool))),X3) = ti(fun(X2,X1),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_3186]) ).

cnf(c_0_3187_0,axiom,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)),X3)
    | ~ comm_semiring_1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3187]) ).

cnf(c_0_3187_1,axiom,
    ( ~ comm_semiring_1(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3187]) ).

cnf(c_0_3188_0,axiom,
    ( hBOOL(hAPP(fun(sum_sum(X1,X2),bool),bool,finite_finite_1(sum_sum(X1,X2)),hAPP(fun(X2,bool),fun(sum_sum(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X2,bool),fun(sum_sum(X1,X2),bool)),sum_Plus(X1,X2),X3),X4)))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3188]) ).

cnf(c_0_3188_1,axiom,
    ( ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
    | hBOOL(hAPP(fun(sum_sum(X1,X2),bool),bool,finite_finite_1(sum_sum(X1,X2)),hAPP(fun(X2,bool),fun(sum_sum(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X2,bool),fun(sum_sum(X1,X2),bool)),sum_Plus(X1,X2),X3),X4)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3188]) ).

cnf(c_0_3188_2,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
    | hBOOL(hAPP(fun(sum_sum(X1,X2),bool),bool,finite_finite_1(sum_sum(X1,X2)),hAPP(fun(X2,bool),fun(sum_sum(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X2,bool),fun(sum_sum(X1,X2),bool)),sum_Plus(X1,X2),X3),X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_3188]) ).

cnf(c_0_3189_0,axiom,
    ( hBOOL(hAPP(fun(sum_sum(X1,X2),bool),bool,finite_finite_1(sum_sum(X1,X2)),hAPP(fun(X2,bool),fun(sum_sum(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X2,bool),fun(sum_sum(X1,X2),bool)),sum_Plus(X1,X2),X3),X4)))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3189]) ).

cnf(c_0_3189_1,axiom,
    ( ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
    | hBOOL(hAPP(fun(sum_sum(X1,X2),bool),bool,finite_finite_1(sum_sum(X1,X2)),hAPP(fun(X2,bool),fun(sum_sum(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X2,bool),fun(sum_sum(X1,X2),bool)),sum_Plus(X1,X2),X3),X4)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3189]) ).

cnf(c_0_3189_2,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
    | hBOOL(hAPP(fun(sum_sum(X1,X2),bool),bool,finite_finite_1(sum_sum(X1,X2)),hAPP(fun(X2,bool),fun(sum_sum(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X2,bool),fun(sum_sum(X1,X2),bool)),sum_Plus(X1,X2),X3),X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_3189]) ).

cnf(c_0_3190_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X4),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3190]) ).

cnf(c_0_3190_1,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X4),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3190]) ).

cnf(c_0_3190_2,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X4),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3190]) ).

cnf(c_0_3191_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3191]) ).

cnf(c_0_3191_1,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3191]) ).

cnf(c_0_3191_2,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3191]) ).

cnf(c_0_3192_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3192]) ).

cnf(c_0_3192_1,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3192]) ).

cnf(c_0_3192_2,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3192]) ).

cnf(c_0_3193_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3193]) ).

cnf(c_0_3193_1,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3193]) ).

cnf(c_0_3193_2,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3193]) ).

cnf(c_0_3194_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3194]) ).

cnf(c_0_3194_1,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3194]) ).

cnf(c_0_3194_2,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X4))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3194]) ).

cnf(c_0_3195_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_3195]) ).

cnf(c_0_3195_1,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_3195]) ).

cnf(c_0_3195_2,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_3195]) ).

cnf(c_0_3195_3,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3195]) ).

cnf(c_0_3196_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3196]) ).

cnf(c_0_3196_1,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3196]) ).

cnf(c_0_3196_2,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3196]) ).

cnf(c_0_3196_3,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3196]) ).

cnf(c_0_3197_0,axiom,
    ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,X1))
    | hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),sk1_esk15_1(X1)),arrow_1111136790e_Prof)) ),
    inference(literals_permutation,[status(thm)],[c_0_3197]) ).

cnf(c_0_3197_1,axiom,
    ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),sk1_esk15_1(X1)),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_3197]) ).

cnf(c_0_3198_0,axiom,
    ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1))
    | hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),sk1_esk10_1(X1)),arrow_1111136790e_Prof)) ),
    inference(literals_permutation,[status(thm)],[c_0_3198]) ).

cnf(c_0_3198_1,axiom,
    ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),sk1_esk10_1(X1)),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_3198]) ).

cnf(c_0_3199_0,axiom,
    ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1))
    | hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),sk1_esk11_1(X1)),arrow_1111136790e_Prof)) ),
    inference(literals_permutation,[status(thm)],[c_0_3199]) ).

cnf(c_0_3199_1,axiom,
    ( hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),sk1_esk11_1(X1)),arrow_1111136790e_Prof))
    | hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_3199]) ).

cnf(c_0_3200_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X3,X4)),hAPP(X2,X1,X5,X4)))
    | ~ ord(X1)
    | ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_3200]) ).

cnf(c_0_3200_1,axiom,
    ( ~ ord(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X3,X4)),hAPP(X2,X1,X5,X4)))
    | ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X5)) ),
    inference(literals_permutation,[status(thm)],[c_0_3200]) ).

cnf(c_0_3200_2,axiom,
    ( ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X5))
    | ~ ord(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X3,X4)),hAPP(X2,X1,X5,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_3200]) ).

cnf(c_0_3201_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X3,X4)),hAPP(X2,X1,X5,X4)))
    | ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X5))
    | ~ ord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3201]) ).

cnf(c_0_3201_1,axiom,
    ( ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X5))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X3,X4)),hAPP(X2,X1,X5,X4)))
    | ~ ord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3201]) ).

cnf(c_0_3201_2,axiom,
    ( ~ ord(X1)
    | ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X5))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X3,X4)),hAPP(X2,X1,X5,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_3201]) ).

cnf(c_0_3202_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X3,X4)),hAPP(X2,X1,X5,X4)))
    | ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X5))
    | ~ ord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3202]) ).

cnf(c_0_3202_1,axiom,
    ( ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X5))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X3,X4)),hAPP(X2,X1,X5,X4)))
    | ~ ord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3202]) ).

cnf(c_0_3202_2,axiom,
    ( ~ ord(X1)
    | ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X5))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),hAPP(X2,X1,X3,X4)),hAPP(X2,X1,X5,X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_3202]) ).

cnf(c_0_3203_0,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X2)),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_3203]) ).

cnf(c_0_3203_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X2)),X1))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3203]) ).

cnf(c_0_3204_0,axiom,
    ( ti(X1,X2) = ti(X1,X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),X2))
    | hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X5),X2) != hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X3)
    | ~ linorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3204]) ).

cnf(c_0_3204_1,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
    | ti(X1,X2) = ti(X1,X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),X2))
    | hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X5),X2) != hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X3)
    | ~ linorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3204]) ).

cnf(c_0_3204_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
    | ti(X1,X2) = ti(X1,X3)
    | hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X5),X2) != hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X3)
    | ~ linorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3204]) ).

cnf(c_0_3204_3,axiom,
    ( hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X5),X2) != hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
    | ti(X1,X2) = ti(X1,X3)
    | ~ linorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3204]) ).

cnf(c_0_3204_4,axiom,
    ( ~ linorder(X1)
    | hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X5),X2) != hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
    | ti(X1,X2) = ti(X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3204]) ).

cnf(c_0_3205_0,axiom,
    ( ti(X1,X2) = ti(X1,X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X5))
    | hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X5) != hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X3),X4)
    | ~ linorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3205]) ).

cnf(c_0_3205_1,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
    | ti(X1,X2) = ti(X1,X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X5))
    | hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X5) != hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X3),X4)
    | ~ linorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3205]) ).

cnf(c_0_3205_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
    | ti(X1,X2) = ti(X1,X3)
    | hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X5) != hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X3),X4)
    | ~ linorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3205]) ).

cnf(c_0_3205_3,axiom,
    ( hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X5) != hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X3),X4)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
    | ti(X1,X2) = ti(X1,X3)
    | ~ linorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3205]) ).

cnf(c_0_3205_4,axiom,
    ( ~ linorder(X1)
    | hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X5) != hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X3),X4)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X4))
    | ti(X1,X2) = ti(X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3205]) ).

cnf(c_0_3206_0,axiom,
    ( ti(X1,X2) = ti(X1,X4)
    | ~ linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X5))
    | hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X3) != hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5) ),
    inference(literals_permutation,[status(thm)],[c_0_3206]) ).

cnf(c_0_3206_1,axiom,
    ( ~ linorder(X1)
    | ti(X1,X2) = ti(X1,X4)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X5))
    | hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X3) != hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5) ),
    inference(literals_permutation,[status(thm)],[c_0_3206]) ).

cnf(c_0_3206_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ linorder(X1)
    | ti(X1,X2) = ti(X1,X4)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X5))
    | hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X3) != hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5) ),
    inference(literals_permutation,[status(thm)],[c_0_3206]) ).

cnf(c_0_3206_3,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ linorder(X1)
    | ti(X1,X2) = ti(X1,X4)
    | hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X3) != hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5) ),
    inference(literals_permutation,[status(thm)],[c_0_3206]) ).

cnf(c_0_3206_4,axiom,
    ( hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X3) != hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ linorder(X1)
    | ti(X1,X2) = ti(X1,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_3206]) ).

cnf(c_0_3207_0,axiom,
    ( ti(X1,X3) = ti(X1,X5)
    | ~ linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X5))
    | hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X3) != hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5) ),
    inference(literals_permutation,[status(thm)],[c_0_3207]) ).

cnf(c_0_3207_1,axiom,
    ( ~ linorder(X1)
    | ti(X1,X3) = ti(X1,X5)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X5))
    | hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X3) != hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5) ),
    inference(literals_permutation,[status(thm)],[c_0_3207]) ).

cnf(c_0_3207_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ linorder(X1)
    | ti(X1,X3) = ti(X1,X5)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X5))
    | hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X3) != hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5) ),
    inference(literals_permutation,[status(thm)],[c_0_3207]) ).

cnf(c_0_3207_3,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ linorder(X1)
    | ti(X1,X3) = ti(X1,X5)
    | hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X3) != hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5) ),
    inference(literals_permutation,[status(thm)],[c_0_3207]) ).

cnf(c_0_3207_4,axiom,
    ( hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X3) != hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ linorder(X1)
    | ti(X1,X3) = ti(X1,X5) ),
    inference(literals_permutation,[status(thm)],[c_0_3207]) ).

cnf(c_0_3208_0,axiom,
    ( hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less(fun(X2,X1)),X3),X4))
    | hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X4),X3))
    | ~ ord(X1)
    | ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3208]) ).

cnf(c_0_3208_1,axiom,
    ( hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X4),X3))
    | hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less(fun(X2,X1)),X3),X4))
    | ~ ord(X1)
    | ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3208]) ).

cnf(c_0_3208_2,axiom,
    ( ~ ord(X1)
    | hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X4),X3))
    | hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less(fun(X2,X1)),X3),X4))
    | ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3208]) ).

cnf(c_0_3208_3,axiom,
    ( ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X4))
    | ~ ord(X1)
    | hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X4),X3))
    | hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less(fun(X2,X1)),X3),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3208]) ).

cnf(c_0_3209_0,axiom,
    ( hBOOL(hAPP(fun(X1,fun(X2,bool)),bool,hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,fun(X2,bool)),bool),ord_less_eq(fun(X1,fun(X2,bool))),X3),X4))
    | hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X3,sk1_esk50_4(X2,X1,X4,X3)),sk1_esk51_4(X2,X1,X4,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_3209]) ).

cnf(c_0_3209_1,axiom,
    ( hBOOL(hAPP(X2,bool,hAPP(X1,fun(X2,bool),X3,sk1_esk50_4(X2,X1,X4,X3)),sk1_esk51_4(X2,X1,X4,X3)))
    | hBOOL(hAPP(fun(X1,fun(X2,bool)),bool,hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,fun(X2,bool)),bool),ord_less_eq(fun(X1,fun(X2,bool))),X3),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3209]) ).

cnf(c_0_3210_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),sk1_esk38_4(X1,X4,X2,X3)),X3))
    | ~ dense_linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3210]) ).

cnf(c_0_3210_1,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),sk1_esk38_4(X1,X4,X2,X3)),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
    | ~ dense_linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3210]) ).

cnf(c_0_3210_2,axiom,
    ( ~ dense_linorder(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),sk1_esk38_4(X1,X4,X2,X3)),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3210]) ).

cnf(c_0_3210_3,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ dense_linorder(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),sk1_esk38_4(X1,X4,X2,X3)),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3210]) ).

cnf(c_0_3211_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)))
    | ~ linord219039673up_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3211]) ).

cnf(c_0_3211_1,axiom,
    ( ~ linord219039673up_add(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3211]) ).

cnf(c_0_3211_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),X2))
    | ~ linord219039673up_add(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_3211]) ).

cnf(c_0_3212_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)))
    | ~ linord219039673up_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3212]) ).

cnf(c_0_3212_1,axiom,
    ( ~ linord219039673up_add(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2)))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3212]) ).

cnf(c_0_3212_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
    | ~ linord219039673up_add(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_3212]) ).

cnf(c_0_3213_0,axiom,
    ( hAPP(fun(sum_sum(X1,X2),bool),nat,finite_card(sum_sum(X1,X2)),hAPP(fun(X2,bool),fun(sum_sum(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X2,bool),fun(sum_sum(X1,X2),bool)),sum_Plus(X1,X2),X3),X4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X3)),hAPP(fun(X2,bool),nat,finite_card(X2),X4))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3213]) ).

cnf(c_0_3213_1,axiom,
    ( ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
    | hAPP(fun(sum_sum(X1,X2),bool),nat,finite_card(sum_sum(X1,X2)),hAPP(fun(X2,bool),fun(sum_sum(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X2,bool),fun(sum_sum(X1,X2),bool)),sum_Plus(X1,X2),X3),X4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X3)),hAPP(fun(X2,bool),nat,finite_card(X2),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3213]) ).

cnf(c_0_3213_2,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
    | hAPP(fun(sum_sum(X1,X2),bool),nat,finite_card(sum_sum(X1,X2)),hAPP(fun(X2,bool),fun(sum_sum(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X2,bool),fun(sum_sum(X1,X2),bool)),sum_Plus(X1,X2),X3),X4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X3)),hAPP(fun(X2,bool),nat,finite_card(X2),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3213]) ).

cnf(c_0_3214_0,axiom,
    ( hAPP(fun(sum_sum(X1,X2),bool),nat,finite_card(sum_sum(X1,X2)),hAPP(fun(X2,bool),fun(sum_sum(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X2,bool),fun(sum_sum(X1,X2),bool)),sum_Plus(X1,X2),X3),X4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X3)),hAPP(fun(X2,bool),nat,finite_card(X2),X4))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3214]) ).

cnf(c_0_3214_1,axiom,
    ( ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
    | hAPP(fun(sum_sum(X1,X2),bool),nat,finite_card(sum_sum(X1,X2)),hAPP(fun(X2,bool),fun(sum_sum(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X2,bool),fun(sum_sum(X1,X2),bool)),sum_Plus(X1,X2),X3),X4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X3)),hAPP(fun(X2,bool),nat,finite_card(X2),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3214]) ).

cnf(c_0_3214_2,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
    | hAPP(fun(sum_sum(X1,X2),bool),nat,finite_card(sum_sum(X1,X2)),hAPP(fun(X2,bool),fun(sum_sum(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X2,bool),fun(sum_sum(X1,X2),bool)),sum_Plus(X1,X2),X3),X4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X1,bool),nat,finite_card(X1),X3)),hAPP(fun(X2,bool),nat,finite_card(X2),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3214]) ).

cnf(c_0_3215_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X4),X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | hAPP(fun(X3,bool),nat,finite_card(X3),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X4),X2)) != hAPP(fun(X1,bool),nat,finite_card(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3215]) ).

cnf(c_0_3215_1,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X4),X2))
    | hAPP(fun(X3,bool),nat,finite_card(X3),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X4),X2)) != hAPP(fun(X1,bool),nat,finite_card(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3215]) ).

cnf(c_0_3215_2,axiom,
    ( hAPP(fun(X3,bool),nat,finite_card(X3),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X4),X2)) != hAPP(fun(X1,bool),nat,finite_card(X1),X2)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X4),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3215]) ).

cnf(c_0_3216_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | hAPP(fun(X2,bool),nat,finite_card(X2),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X4)) != hAPP(fun(X1,bool),nat,finite_card(X1),X4)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3216]) ).

cnf(c_0_3216_1,axiom,
    ( hAPP(fun(X2,bool),nat,finite_card(X2),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X4)) != hAPP(fun(X1,bool),nat,finite_card(X1),X4)
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3216]) ).

cnf(c_0_3216_2,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X4))
    | hAPP(fun(X2,bool),nat,finite_card(X2),hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),X4)) != hAPP(fun(X1,bool),nat,finite_card(X1),X4)
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3216]) ).

cnf(c_0_3217_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_3217]) ).

cnf(c_0_3217_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_3217]) ).

cnf(c_0_3218_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3218]) ).

cnf(c_0_3218_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_3218]) ).

cnf(c_0_3219_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3219]) ).

cnf(c_0_3219_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_3219]) ).

cnf(c_0_3220_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3220]) ).

cnf(c_0_3220_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X3))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_3220]) ).

cnf(c_0_3221_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3221]) ).

cnf(c_0_3221_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_3221]) ).

cnf(c_0_3222_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3222]) ).

cnf(c_0_3222_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_3222]) ).

cnf(c_0_3223_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3223]) ).

cnf(c_0_3223_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_3223]) ).

cnf(c_0_3224_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3224]) ).

cnf(c_0_3224_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_3224]) ).

cnf(c_0_3225_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3225]) ).

cnf(c_0_3225_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X3))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_3225]) ).

cnf(c_0_3226_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3226]) ).

cnf(c_0_3226_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_3226]) ).

cnf(c_0_3227_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_3227]) ).

cnf(c_0_3227_1,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_3227]) ).

cnf(c_0_3227_2,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_3227]) ).

cnf(c_0_3227_3,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3227]) ).

cnf(c_0_3228_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),sk1_esk94_2(X1,X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3228]) ).

cnf(c_0_3228_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),sk1_esk94_2(X1,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_3228]) ).

cnf(c_0_3229_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3229]) ).

cnf(c_0_3229_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3229]) ).

cnf(c_0_3230_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3230]) ).

cnf(c_0_3230_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3230]) ).

cnf(c_0_3231_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3231]) ).

cnf(c_0_3231_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3231]) ).

cnf(c_0_3232_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3232]) ).

cnf(c_0_3232_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3232]) ).

cnf(c_0_3233_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3233]) ).

cnf(c_0_3233_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3233]) ).

cnf(c_0_3234_0,axiom,
    ( hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X3) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5)
    | ~ linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X5))
    | ti(X1,X3) != ti(X1,X5)
    | ti(X1,X2) != ti(X1,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_3234]) ).

cnf(c_0_3234_1,axiom,
    ( ~ linorder(X1)
    | hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X3) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X5))
    | ti(X1,X3) != ti(X1,X5)
    | ti(X1,X2) != ti(X1,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_3234]) ).

cnf(c_0_3234_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ linorder(X1)
    | hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X3) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X5))
    | ti(X1,X3) != ti(X1,X5)
    | ti(X1,X2) != ti(X1,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_3234]) ).

cnf(c_0_3234_3,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ linorder(X1)
    | hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X3) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5)
    | ti(X1,X3) != ti(X1,X5)
    | ti(X1,X2) != ti(X1,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_3234]) ).

cnf(c_0_3234_4,axiom,
    ( ti(X1,X3) != ti(X1,X5)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ linorder(X1)
    | hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X3) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5)
    | ti(X1,X2) != ti(X1,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_3234]) ).

cnf(c_0_3234_5,axiom,
    ( ti(X1,X2) != ti(X1,X4)
    | ti(X1,X3) != ti(X1,X5)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X5))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ linorder(X1)
    | hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X2),X3) = hAPP(X1,fun(X1,bool),hAPP(X1,fun(X1,fun(X1,bool)),ord_atLeastLessThan(X1),X4),X5) ),
    inference(literals_permutation,[status(thm)],[c_0_3234]) ).

cnf(c_0_3235_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),top_top(fun(X3,bool)))))
    | ti(X1,X2) != hAPP(X3,X1,X4,X5) ),
    inference(literals_permutation,[status(thm)],[c_0_3235]) ).

cnf(c_0_3235_1,axiom,
    ( ti(X1,X2) != hAPP(X3,X1,X4,X5)
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),hAPP(fun(X3,bool),fun(X1,bool),hAPP(fun(X3,X1),fun(fun(X3,bool),fun(X1,bool)),image(X3,X1),X4),top_top(fun(X3,bool))))) ),
    inference(literals_permutation,[status(thm)],[c_0_3235]) ).

cnf(c_0_3236_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),hAPP(nat,nat,suc,X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3236]) ).

cnf(c_0_3236_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),hAPP(nat,nat,suc,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_3236]) ).

cnf(c_0_3237_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),hAPP(nat,nat,suc,X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3237]) ).

cnf(c_0_3237_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),hAPP(nat,nat,suc,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_3237]) ).

cnf(c_0_3238_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),hAPP(nat,nat,suc,X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3238]) ).

cnf(c_0_3238_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),hAPP(nat,nat,suc,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_3238]) ).

cnf(c_0_3239_0,axiom,
    ( hAPP(fun(X3,bool),nat,finite_card(X3),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X4),X2)) = hAPP(fun(X1,bool),nat,finite_card(X1),X2)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X4),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3239]) ).

cnf(c_0_3239_1,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | hAPP(fun(X3,bool),nat,finite_card(X3),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X4),X2)) = hAPP(fun(X1,bool),nat,finite_card(X1),X2)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X4),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3239]) ).

cnf(c_0_3239_2,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X3),fun(fun(X1,bool),bool),inj_on(X1,X3),X4),X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | hAPP(fun(X3,bool),nat,finite_card(X3),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X4),X2)) = hAPP(fun(X1,bool),nat,finite_card(X1),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3239]) ).

cnf(c_0_3240_0,axiom,
    ( ~ ord(X1)
    | ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less(fun(X2,X1)),X3),X4))
    | ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X4),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3240]) ).

cnf(c_0_3240_1,axiom,
    ( ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less(fun(X2,X1)),X3),X4))
    | ~ ord(X1)
    | ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X4),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3240]) ).

cnf(c_0_3240_2,axiom,
    ( ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X4),X3))
    | ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less(fun(X2,X1)),X3),X4))
    | ~ ord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3240]) ).

cnf(c_0_3241_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),sk1_esk38_4(X1,X4,X2,X3)))
    | ~ dense_linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3241]) ).

cnf(c_0_3241_1,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),sk1_esk38_4(X1,X4,X2,X3)))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
    | ~ dense_linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3241]) ).

cnf(c_0_3241_2,axiom,
    ( ~ dense_linorder(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),sk1_esk38_4(X1,X4,X2,X3)))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3241]) ).

cnf(c_0_3241_3,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ dense_linorder(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),sk1_esk38_4(X1,X4,X2,X3)))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3241]) ).

cnf(c_0_3242_0,axiom,
    ( ti(fun(X1,bool),X2) = ti(fun(X1,bool),X3)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3242]) ).

cnf(c_0_3242_1,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X2))
    | ti(fun(X1,bool),X2) = ti(fun(X1,bool),X3)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3242]) ).

cnf(c_0_3242_2,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X2))
    | ti(fun(X1,bool),X2) = ti(fun(X1,bool),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3242]) ).

cnf(c_0_3243_0,axiom,
    ( ti(fun(X1,bool),X2) = ti(fun(X1,bool),X3)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3243]) ).

cnf(c_0_3243_1,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X2))
    | ti(fun(X1,bool),X2) = ti(fun(X1,bool),X3)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3243]) ).

cnf(c_0_3243_2,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X2))
    | ti(fun(X1,bool),X2) = ti(fun(X1,bool),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3243]) ).

cnf(c_0_3244_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
    | ~ order(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3244]) ).

cnf(c_0_3244_1,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
    | ~ order(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3244]) ).

cnf(c_0_3244_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ order(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3244]) ).

cnf(c_0_3244_3,axiom,
    ( ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3244]) ).

cnf(c_0_3245_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | ~ preorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3245]) ).

cnf(c_0_3245_1,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | ~ preorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3245]) ).

cnf(c_0_3245_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ preorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3245]) ).

cnf(c_0_3245_3,axiom,
    ( ~ preorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3245]) ).

cnf(c_0_3246_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
    | ~ order(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3246]) ).

cnf(c_0_3246_1,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
    | ~ order(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3246]) ).

cnf(c_0_3246_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ order(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3246]) ).

cnf(c_0_3246_3,axiom,
    ( ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3246]) ).

cnf(c_0_3247_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | ~ preorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3247]) ).

cnf(c_0_3247_1,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | ~ preorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3247]) ).

cnf(c_0_3247_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ preorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3247]) ).

cnf(c_0_3247_3,axiom,
    ( ~ preorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3247]) ).

cnf(c_0_3248_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | ~ preorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3248]) ).

cnf(c_0_3248_1,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | ~ preorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3248]) ).

cnf(c_0_3248_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ preorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3248]) ).

cnf(c_0_3248_3,axiom,
    ( ~ preorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3248]) ).

cnf(c_0_3249_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
    | ~ order(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3249]) ).

cnf(c_0_3249_1,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
    | ~ order(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3249]) ).

cnf(c_0_3249_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ order(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3249]) ).

cnf(c_0_3249_3,axiom,
    ( ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3249]) ).

cnf(c_0_3250_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | ~ preorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3250]) ).

cnf(c_0_3250_1,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | ~ preorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3250]) ).

cnf(c_0_3250_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ preorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3250]) ).

cnf(c_0_3250_3,axiom,
    ( ~ preorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3250]) ).

cnf(c_0_3251_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
    | ~ order(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3251]) ).

cnf(c_0_3251_1,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
    | ~ order(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3251]) ).

cnf(c_0_3251_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ order(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3251]) ).

cnf(c_0_3251_3,axiom,
    ( ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3251]) ).

cnf(c_0_3252_0,axiom,
    ( hAPP(X1,X2,hAPP(fun(X2,X1),fun(X1,X2),hAPP(fun(X2,bool),fun(fun(X2,X1),fun(X1,X2)),hilbert_inv_into(X2,X1),top_top(fun(X2,bool))),X3),hAPP(X2,X1,X3,X4)) = ti(X2,X4)
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),inj_on(X2,X1),X3),top_top(fun(X2,bool)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3252]) ).

cnf(c_0_3252_1,axiom,
    ( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),inj_on(X2,X1),X3),top_top(fun(X2,bool))))
    | hAPP(X1,X2,hAPP(fun(X2,X1),fun(X1,X2),hAPP(fun(X2,bool),fun(fun(X2,X1),fun(X1,X2)),hilbert_inv_into(X2,X1),top_top(fun(X2,bool))),X3),hAPP(X2,X1,X3,X4)) = ti(X2,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_3252]) ).

cnf(c_0_3254_0,axiom,
    ( hAPP(X1,X2,hAPP(fun(X2,X1),fun(X1,X2),hAPP(fun(X2,bool),fun(fun(X2,X1),fun(X1,X2)),hilbert_inv_into(X2,X1),top_top(fun(X2,bool))),X3),X4) = ti(X2,X5)
    | hAPP(X2,X1,X3,X5) != ti(X1,X4)
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),inj_on(X2,X1),X3),top_top(fun(X2,bool)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3254]) ).

cnf(c_0_3254_1,axiom,
    ( hAPP(X2,X1,X3,X5) != ti(X1,X4)
    | hAPP(X1,X2,hAPP(fun(X2,X1),fun(X1,X2),hAPP(fun(X2,bool),fun(fun(X2,X1),fun(X1,X2)),hilbert_inv_into(X2,X1),top_top(fun(X2,bool))),X3),X4) = ti(X2,X5)
    | ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),inj_on(X2,X1),X3),top_top(fun(X2,bool)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3254]) ).

cnf(c_0_3254_2,axiom,
    ( ~ hBOOL(hAPP(fun(X2,bool),bool,hAPP(fun(X2,X1),fun(fun(X2,bool),bool),inj_on(X2,X1),X3),top_top(fun(X2,bool))))
    | hAPP(X2,X1,X3,X5) != ti(X1,X4)
    | hAPP(X1,X2,hAPP(fun(X2,X1),fun(X1,X2),hAPP(fun(X2,bool),fun(fun(X2,X1),fun(X1,X2)),hilbert_inv_into(X2,X1),top_top(fun(X2,bool))),X3),X4) = ti(X2,X5) ),
    inference(literals_permutation,[status(thm)],[c_0_3254]) ).

cnf(c_0_3255_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3255]) ).

cnf(c_0_3255_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3255]) ).

cnf(c_0_3255_2,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3255]) ).

cnf(c_0_3257_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X3) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4),X2)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3257]) ).

cnf(c_0_3257_1,axiom,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X3) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4),X2)
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3257]) ).

cnf(c_0_3257_2,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X4),X3))
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X3) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X4),X2)
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3257]) ).

cnf(c_0_3258_0,axiom,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4))
    | ~ comm_semiring_1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3258]) ).

cnf(c_0_3258_1,axiom,
    ( ~ comm_semiring_1(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3258]) ).

cnf(c_0_3259_0,axiom,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4))
    | ~ comm_semiring_1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3259]) ).

cnf(c_0_3259_1,axiom,
    ( ~ comm_semiring_1(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3259]) ).

cnf(c_0_3260_0,axiom,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4))
    | ~ ab_semigroup_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3260]) ).

cnf(c_0_3260_1,axiom,
    ( ~ ab_semigroup_add(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3)),X4) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3260]) ).

cnf(c_0_3261_0,axiom,
    ( X2 = X1
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),hAPP(nat,nat,suc,X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_3261]) ).

cnf(c_0_3261_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | X2 = X1
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),hAPP(nat,nat,suc,X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_3261]) ).

cnf(c_0_3261_2,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),hAPP(nat,nat,suc,X1)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | X2 = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_3261]) ).

cnf(c_0_3262_0,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),hAPP(nat,nat,suc,X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_3262]) ).

cnf(c_0_3262_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),hAPP(nat,nat,suc,X1)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3262]) ).

cnf(c_0_3263_0,axiom,
    ( X3 = X2
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3263]) ).

cnf(c_0_3263_1,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
    | X3 = X2
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3263]) ).

cnf(c_0_3263_2,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
    | X3 = X2
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3263]) ).

cnf(c_0_3263_3,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
    | X3 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_3263]) ).

cnf(c_0_3264_0,axiom,
    ( ti(X1,X2) = zero_zero(X1)
    | ~ ordere216010020id_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) != zero_zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3264]) ).

cnf(c_0_3264_1,axiom,
    ( ~ ordere216010020id_add(X1)
    | ti(X1,X2) = zero_zero(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) != zero_zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3264]) ).

cnf(c_0_3264_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
    | ~ ordere216010020id_add(X1)
    | ti(X1,X2) = zero_zero(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) != zero_zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3264]) ).

cnf(c_0_3264_3,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
    | ~ ordere216010020id_add(X1)
    | ti(X1,X2) = zero_zero(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) != zero_zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3264]) ).

cnf(c_0_3264_4,axiom,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) != zero_zero(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
    | ~ ordere216010020id_add(X1)
    | ti(X1,X2) = zero_zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3264]) ).

cnf(c_0_3265_0,axiom,
    ( ti(X1,X3) = zero_zero(X1)
    | ~ ordere216010020id_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) != zero_zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3265]) ).

cnf(c_0_3265_1,axiom,
    ( ~ ordere216010020id_add(X1)
    | ti(X1,X3) = zero_zero(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) != zero_zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3265]) ).

cnf(c_0_3265_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
    | ~ ordere216010020id_add(X1)
    | ti(X1,X3) = zero_zero(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) != zero_zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3265]) ).

cnf(c_0_3265_3,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
    | ~ ordere216010020id_add(X1)
    | ti(X1,X3) = zero_zero(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) != zero_zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3265]) ).

cnf(c_0_3265_4,axiom,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) != zero_zero(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
    | ~ ordere216010020id_add(X1)
    | ti(X1,X3) = zero_zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3265]) ).

cnf(c_0_3267_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),X2))
    | hAPP(nat,nat,suc,X1) = X2
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3267]) ).

cnf(c_0_3267_1,axiom,
    ( hAPP(nat,nat,suc,X1) = X2
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3267]) ).

cnf(c_0_3267_2,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | hAPP(nat,nat,suc,X1) = X2
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3267]) ).

cnf(c_0_3268_0,axiom,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) = zero_zero(X1)
    | ~ ordere216010020id_add(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
    | ti(X1,X3) != zero_zero(X1)
    | ti(X1,X2) != zero_zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3268]) ).

cnf(c_0_3268_1,axiom,
    ( ~ ordere216010020id_add(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) = zero_zero(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
    | ti(X1,X3) != zero_zero(X1)
    | ti(X1,X2) != zero_zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3268]) ).

cnf(c_0_3268_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
    | ~ ordere216010020id_add(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) = zero_zero(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
    | ti(X1,X3) != zero_zero(X1)
    | ti(X1,X2) != zero_zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3268]) ).

cnf(c_0_3268_3,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
    | ~ ordere216010020id_add(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) = zero_zero(X1)
    | ti(X1,X3) != zero_zero(X1)
    | ti(X1,X2) != zero_zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3268]) ).

cnf(c_0_3268_4,axiom,
    ( ti(X1,X3) != zero_zero(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
    | ~ ordere216010020id_add(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) = zero_zero(X1)
    | ti(X1,X2) != zero_zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3268]) ).

cnf(c_0_3268_5,axiom,
    ( ti(X1,X2) != zero_zero(X1)
    | ti(X1,X3) != zero_zero(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),X2))
    | ~ ordere216010020id_add(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) = zero_zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3268]) ).

cnf(c_0_3269_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3269]) ).

cnf(c_0_3269_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3269]) ).

cnf(c_0_3270_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3270]) ).

cnf(c_0_3270_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3270]) ).

cnf(c_0_3271_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3271]) ).

cnf(c_0_3271_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3271]) ).

cnf(c_0_3273_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X4)))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3273]) ).

cnf(c_0_3273_1,axiom,
    ( ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
    | hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),X4))) ),
    inference(literals_permutation,[status(thm)],[c_0_3273]) ).

cnf(c_0_3274_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk69_4(X2,X1,X3,X4)),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3274]) ).

cnf(c_0_3274_1,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk69_4(X2,X1,X3,X4)),X4))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3274]) ).

cnf(c_0_3275_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk70_4(X2,X1,X3,X4)),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3275]) ).

cnf(c_0_3275_1,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk70_4(X2,X1,X3,X4)),X4))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3275]) ).

cnf(c_0_3276_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk30_4(X1,X2,X3,X4)),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3276]) ).

cnf(c_0_3276_1,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk30_4(X1,X2,X3,X4)),X4))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3276]) ).

cnf(c_0_3277_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk31_4(X1,X2,X3,X4)),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3277]) ).

cnf(c_0_3277_1,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk31_4(X1,X2,X3,X4)),X4))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3277]) ).

cnf(c_0_3278_0,axiom,
    ( X1 = hAPP(nat,nat,suc,X2)
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,suc,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_3278]) ).

cnf(c_0_3278_1,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | X1 = hAPP(nat,nat,suc,X2)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,suc,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_3278]) ).

cnf(c_0_3278_2,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,suc,X2)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | X1 = hAPP(nat,nat,suc,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3278]) ).

cnf(c_0_3279_0,axiom,
    ( X1 = hAPP(nat,nat,suc,X2)
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,suc,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_3279]) ).

cnf(c_0_3279_1,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | X1 = hAPP(nat,nat,suc,X2)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,suc,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_3279]) ).

cnf(c_0_3279_2,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,suc,X2)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | X1 = hAPP(nat,nat,suc,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3279]) ).

cnf(c_0_3280_0,axiom,
    ( hAPP(nat,nat,suc,sk1_esk94_2(X1,X2)) = X2
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3280]) ).

cnf(c_0_3280_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,X1)),X2))
    | hAPP(nat,nat,suc,sk1_esk94_2(X1,X2)) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_3280]) ).

cnf(c_0_3281_0,axiom,
    ( hAPP(nat,nat,suc,sk1_esk92_2(X2,X1)) = X1
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X2)),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_3281]) ).

cnf(c_0_3281_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X2)),X1))
    | hAPP(nat,nat,suc,sk1_esk92_2(X2,X1)) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_3281]) ).

cnf(c_0_3282_0,axiom,
    ( hBOOL(hAPP(nat,bool,X3,X1))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sk1_esk86_3(X3,X1,X2)),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,X3,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3282]) ).

cnf(c_0_3282_1,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sk1_esk86_3(X3,X1,X2)),X2))
    | hBOOL(hAPP(nat,bool,X3,X1))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,X3,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3282]) ).

cnf(c_0_3282_2,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sk1_esk86_3(X3,X1,X2)),X2))
    | hBOOL(hAPP(nat,bool,X3,X1))
    | ~ hBOOL(hAPP(nat,bool,X3,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3282]) ).

cnf(c_0_3282_3,axiom,
    ( ~ hBOOL(hAPP(nat,bool,X3,X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sk1_esk86_3(X3,X1,X2)),X2))
    | hBOOL(hAPP(nat,bool,X3,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_3282]) ).

cnf(c_0_3283_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ preorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3283]) ).

cnf(c_0_3283_1,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ preorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3283]) ).

cnf(c_0_3283_2,axiom,
    ( ~ preorder(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3283]) ).

cnf(c_0_3283_3,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ preorder(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3283]) ).

cnf(c_0_3285_0,axiom,
    ( X1 = zero_zero(nat)
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sk1_esk85_2(X1,X2)),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_3285]) ).

cnf(c_0_3285_1,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sk1_esk85_2(X1,X2)),X2))
    | X1 = zero_zero(nat)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_3285]) ).

cnf(c_0_3285_2,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sk1_esk85_2(X1,X2)),X2))
    | X1 = zero_zero(nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3285]) ).

cnf(c_0_3286_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk53_3(X1,X3,X2)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3286]) ).

cnf(c_0_3286_1,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk53_3(X1,X3,X2)),X3))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3286]) ).

cnf(c_0_3287_0,axiom,
    ( hBOOL(hAPP(product_prod(X1,X2),bool,X3,hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X4),X5)))
    | ~ hBOOL(hAPP(product_prod(X1,X2),bool,X3,sk1_esk6_3(X1,X2,X3))) ),
    inference(literals_permutation,[status(thm)],[c_0_3287]) ).

cnf(c_0_3287_1,axiom,
    ( ~ hBOOL(hAPP(product_prod(X1,X2),bool,X3,sk1_esk6_3(X1,X2,X3)))
    | hBOOL(hAPP(product_prod(X1,X2),bool,X3,hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X4),X5))) ),
    inference(literals_permutation,[status(thm)],[c_0_3287]) ).

cnf(c_0_3288_0,axiom,
    ( hBOOL(hAPP(nat,bool,X3,X1))
    | hBOOL(hAPP(nat,bool,X3,hAPP(nat,nat,suc,sk1_esk86_3(X3,X1,X2))))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,X3,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3288]) ).

cnf(c_0_3288_1,axiom,
    ( hBOOL(hAPP(nat,bool,X3,hAPP(nat,nat,suc,sk1_esk86_3(X3,X1,X2))))
    | hBOOL(hAPP(nat,bool,X3,X1))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,X3,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3288]) ).

cnf(c_0_3288_2,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,X3,hAPP(nat,nat,suc,sk1_esk86_3(X3,X1,X2))))
    | hBOOL(hAPP(nat,bool,X3,X1))
    | ~ hBOOL(hAPP(nat,bool,X3,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3288]) ).

cnf(c_0_3288_3,axiom,
    ( ~ hBOOL(hAPP(nat,bool,X3,X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,X3,hAPP(nat,nat,suc,sk1_esk86_3(X3,X1,X2))))
    | hBOOL(hAPP(nat,bool,X3,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_3288]) ).

cnf(c_0_3289_0,axiom,
    ( hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X4))
    | ~ ord(X1)
    | ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less(fun(X2,X1)),X3),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3289]) ).

cnf(c_0_3289_1,axiom,
    ( ~ ord(X1)
    | hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X4))
    | ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less(fun(X2,X1)),X3),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3289]) ).

cnf(c_0_3289_2,axiom,
    ( ~ hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less(fun(X2,X1)),X3),X4))
    | ~ ord(X1)
    | hBOOL(hAPP(fun(X2,X1),bool,hAPP(fun(X2,X1),fun(fun(X2,X1),bool),ord_less_eq(fun(X2,X1)),X3),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3289]) ).

cnf(c_0_3290_0,axiom,
    ( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X2),top_top(fun(X1,bool))) = top_top(fun(X1,bool))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X2),top_top(fun(X1,bool))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3290]) ).

cnf(c_0_3290_1,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X2),top_top(fun(X1,bool))))
    | hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X2),top_top(fun(X1,bool))) = top_top(fun(X1,bool))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3290]) ).

cnf(c_0_3290_2,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X2),top_top(fun(X1,bool))))
    | hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X2),top_top(fun(X1,bool))) = top_top(fun(X1,bool)) ),
    inference(literals_permutation,[status(thm)],[c_0_3290]) ).

cnf(c_0_3291_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | X1 = X2
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_3291]) ).

cnf(c_0_3291_1,axiom,
    ( X1 = X2
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_3291]) ).

cnf(c_0_3291_2,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
    | X1 = X2
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_3291]) ).

cnf(c_0_3291_3,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
    | X1 = X2
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3291]) ).

cnf(c_0_3292_0,axiom,
    ( X3 = X2
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3292]) ).

cnf(c_0_3292_1,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
    | X3 = X2
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3292]) ).

cnf(c_0_3292_2,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
    | X3 = X2
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3292]) ).

cnf(c_0_3292_3,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X3))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X1,X2),X3))
    | X3 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_3292]) ).

cnf(c_0_3293_0,axiom,
    ( X1 = X2
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_3293]) ).

cnf(c_0_3293_1,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | X1 = X2
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_3293]) ).

cnf(c_0_3293_2,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_3293]) ).

cnf(c_0_3294_0,axiom,
    ( X1 = X2
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),hAPP(nat,nat,suc,X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_3294]) ).

cnf(c_0_3294_1,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1))
    | X1 = X2
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),hAPP(nat,nat,suc,X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_3294]) ).

cnf(c_0_3294_2,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),hAPP(nat,nat,suc,X1)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1))
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_3294]) ).

cnf(c_0_3295_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | X1 = X2
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_3295]) ).

cnf(c_0_3295_1,axiom,
    ( X1 = X2
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_3295]) ).

cnf(c_0_3295_2,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2)))
    | X1 = X2
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3295]) ).

cnf(c_0_3296_0,axiom,
    ( X1 = X2
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_3296]) ).

cnf(c_0_3296_1,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | X1 = X2
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_3296]) ).

cnf(c_0_3296_2,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_3296]) ).

cnf(c_0_3297_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_3297]) ).

cnf(c_0_3297_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3297]) ).

cnf(c_0_3299_0,axiom,
    ( ti(fun(X1,bool),X2) = ti(fun(X1,bool),X3)
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3299]) ).

cnf(c_0_3299_1,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3))
    | ti(fun(X1,bool),X2) = ti(fun(X1,bool),X3)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3299]) ).

cnf(c_0_3299_2,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3))
    | ti(fun(X1,bool),X2) = ti(fun(X1,bool),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3299]) ).

cnf(c_0_3300_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3))
    | ti(fun(X1,bool),X2) = ti(fun(X1,bool),X3)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3300]) ).

cnf(c_0_3300_1,axiom,
    ( ti(fun(X1,bool),X2) = ti(fun(X1,bool),X3)
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3300]) ).

cnf(c_0_3300_2,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ti(fun(X1,bool),X2) = ti(fun(X1,bool),X3)
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3300]) ).

cnf(c_0_3301_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3301]) ).

cnf(c_0_3301_1,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3301]) ).

cnf(c_0_3302_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3302]) ).

cnf(c_0_3302_1,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3302]) ).

cnf(c_0_3303_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3303]) ).

cnf(c_0_3303_1,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3303]) ).

cnf(c_0_3304_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X2))
    | X1 != hAPP(nat,nat,suc,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3304]) ).

cnf(c_0_3304_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2)))
    | X1 != hAPP(nat,nat,suc,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3304]) ).

cnf(c_0_3304_2,axiom,
    ( X1 != hAPP(nat,nat,suc,X3)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_3304]) ).

cnf(c_0_3305_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),sk1_esk75_1(X2)))
    | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X1),X2))
    | ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3305]) ).

cnf(c_0_3305_1,axiom,
    ( ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),sk1_esk75_1(X2)))
    | ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3305]) ).

cnf(c_0_3305_2,axiom,
    ( ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X2))
    | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),sk1_esk75_1(X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_3305]) ).

cnf(c_0_3306_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),sk1_esk73_1(X2)))
    | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X1),X2))
    | ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3306]) ).

cnf(c_0_3306_1,axiom,
    ( ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),sk1_esk73_1(X2)))
    | ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3306]) ).

cnf(c_0_3306_2,axiom,
    ( ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X2))
    | ~ hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),sk1_esk73_1(X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_3306]) ).

cnf(c_0_3307_0,axiom,
    ( hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
    | hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),sk1_esk79_2(X2,X1)),one_one(nat))))
    | ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3307]) ).

cnf(c_0_3307_1,axiom,
    ( hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),sk1_esk79_2(X2,X1)),one_one(nat))))
    | hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
    | ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3307]) ).

cnf(c_0_3307_2,axiom,
    ( ~ hBOOL(hAPP(nat,bool,X1,X2))
    | hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),sk1_esk79_2(X2,X1)),one_one(nat))))
    | hBOOL(hAPP(nat,bool,X1,zero_zero(nat))) ),
    inference(literals_permutation,[status(thm)],[c_0_3307]) ).

cnf(c_0_3308_0,axiom,
    ( ~ linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X2) != ti(X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3308]) ).

cnf(c_0_3308_1,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X2) != ti(X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3308]) ).

cnf(c_0_3308_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ linorder(X1)
    | ti(X1,X2) != ti(X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3308]) ).

cnf(c_0_3308_3,axiom,
    ( ti(X1,X2) != ti(X1,X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ linorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3308]) ).

cnf(c_0_3309_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_3309]) ).

cnf(c_0_3309_1,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3309]) ).

cnf(c_0_3310_0,axiom,
    ( ti(X1,X2) = ti(X1,X3)
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3310]) ).

cnf(c_0_3310_1,axiom,
    ( ~ order(X1)
    | ti(X1,X2) = ti(X1,X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3310]) ).

cnf(c_0_3310_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ order(X1)
    | ti(X1,X2) = ti(X1,X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3310]) ).

cnf(c_0_3310_3,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ order(X1)
    | ti(X1,X2) = ti(X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3310]) ).

cnf(c_0_3311_0,axiom,
    ( ti(X1,X3) = ti(X1,X2)
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3311]) ).

cnf(c_0_3311_1,axiom,
    ( ~ order(X1)
    | ti(X1,X3) = ti(X1,X2)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3311]) ).

cnf(c_0_3311_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ order(X1)
    | ti(X1,X3) = ti(X1,X2)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3311]) ).

cnf(c_0_3311_3,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ order(X1)
    | ti(X1,X3) = ti(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3311]) ).

cnf(c_0_3312_0,axiom,
    ( ti(X1,X2) = ti(X1,X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ order(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3312]) ).

cnf(c_0_3312_1,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ti(X1,X2) = ti(X1,X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ order(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3312]) ).

cnf(c_0_3312_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ti(X1,X2) = ti(X1,X3)
    | ~ order(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3312]) ).

cnf(c_0_3312_3,axiom,
    ( ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ti(X1,X2) = ti(X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3312]) ).

cnf(c_0_3313_0,axiom,
    ( ti(X1,X2) = ti(X1,X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ order(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3313]) ).

cnf(c_0_3313_1,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ti(X1,X2) = ti(X1,X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ order(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3313]) ).

cnf(c_0_3313_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ti(X1,X2) = ti(X1,X3)
    | ~ order(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3313]) ).

cnf(c_0_3313_3,axiom,
    ( ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ti(X1,X2) = ti(X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3313]) ).

cnf(c_0_3314_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X2),top_top(fun(X1,bool))))
    | hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X2),top_top(fun(X1,bool))) != top_top(fun(X1,bool))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3314]) ).

cnf(c_0_3314_1,axiom,
    ( hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X2),top_top(fun(X1,bool))) != top_top(fun(X1,bool))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X2),top_top(fun(X1,bool))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3314]) ).

cnf(c_0_3314_2,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool))))
    | hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),X2),top_top(fun(X1,bool))) != top_top(fun(X1,bool))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),X2),top_top(fun(X1,bool)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3314]) ).

cnf(c_0_3315_0,axiom,
    ( hBOOL(X1)
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X3),X4))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X4),X3))
    | ~ preorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3315]) ).

cnf(c_0_3315_1,axiom,
    ( ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X3),X4))
    | hBOOL(X1)
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X4),X3))
    | ~ preorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3315]) ).

cnf(c_0_3315_2,axiom,
    ( ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X4),X3))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X3),X4))
    | hBOOL(X1)
    | ~ preorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3315]) ).

cnf(c_0_3315_3,axiom,
    ( ~ preorder(X2)
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X4),X3))
    | ~ hBOOL(hAPP(X2,bool,hAPP(X2,fun(X2,bool),ord_less(X2),X3),X4))
    | hBOOL(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3315]) ).

cnf(c_0_3316_0,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ linorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3316]) ).

cnf(c_0_3316_1,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ linorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3316]) ).

cnf(c_0_3316_2,axiom,
    ( ~ linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3316]) ).

cnf(c_0_3317_0,axiom,
    ( ~ preorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3317]) ).

cnf(c_0_3317_1,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ preorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3317]) ).

cnf(c_0_3317_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ preorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3317]) ).

cnf(c_0_3318_0,axiom,
    ( ~ linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3318]) ).

cnf(c_0_3318_1,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3318]) ).

cnf(c_0_3318_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ linorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3318]) ).

cnf(c_0_3319_0,axiom,
    ( ~ linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3319]) ).

cnf(c_0_3319_1,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3319]) ).

cnf(c_0_3319_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ linorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3319]) ).

cnf(c_0_3320_0,axiom,
    ( ~ linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3320]) ).

cnf(c_0_3320_1,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3320]) ).

cnf(c_0_3320_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ linorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3320]) ).

cnf(c_0_3321_0,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ preorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3321]) ).

cnf(c_0_3321_1,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ preorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3321]) ).

cnf(c_0_3321_2,axiom,
    ( ~ preorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3321]) ).

cnf(c_0_3322_0,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ preorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3322]) ).

cnf(c_0_3322_1,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ preorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3322]) ).

cnf(c_0_3322_2,axiom,
    ( ~ preorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3322]) ).

cnf(c_0_3323_0,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ preorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3323]) ).

cnf(c_0_3323_1,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ preorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3323]) ).

cnf(c_0_3323_2,axiom,
    ( ~ preorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3323]) ).

cnf(c_0_3324_0,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ order(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3324]) ).

cnf(c_0_3324_1,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ order(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3324]) ).

cnf(c_0_3324_2,axiom,
    ( ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3324]) ).

cnf(c_0_3325_0,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ preorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3325]) ).

cnf(c_0_3325_1,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ preorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3325]) ).

cnf(c_0_3325_2,axiom,
    ( ~ preorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3325]) ).

cnf(c_0_3326_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),hAPP(nat,nat,suc,X1)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | X2 != X1 ),
    inference(literals_permutation,[status(thm)],[c_0_3326]) ).

cnf(c_0_3326_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),hAPP(nat,nat,suc,X1)))
    | X2 != X1 ),
    inference(literals_permutation,[status(thm)],[c_0_3326]) ).

cnf(c_0_3326_2,axiom,
    ( X2 != X1
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),hAPP(nat,nat,suc,X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_3326]) ).

cnf(c_0_3327_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3327]) ).

cnf(c_0_3327_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_3327]) ).

cnf(c_0_3328_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3328]) ).

cnf(c_0_3328_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_3328]) ).

cnf(c_0_3329_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3329]) ).

cnf(c_0_3329_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_3329]) ).

cnf(c_0_3330_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3330]) ).

cnf(c_0_3330_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_3330]) ).

cnf(c_0_3331_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,suc,X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3331]) ).

cnf(c_0_3331_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,suc,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_3331]) ).

cnf(c_0_3332_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,suc,X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3332]) ).

cnf(c_0_3332_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,suc,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_3332]) ).

cnf(c_0_3333_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),one_one(X1)),one_one(X1))))
    | ~ linordered_semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3333]) ).

cnf(c_0_3333_1,axiom,
    ( ~ linordered_semidom(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),one_one(X1)),one_one(X1)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3333]) ).

cnf(c_0_3334_0,axiom,
    ( X1 = X2
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3334]) ).

cnf(c_0_3334_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1))
    | X1 = X2
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3334]) ).

cnf(c_0_3334_2,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1))
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_3334]) ).

cnf(c_0_3335_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),one_one(X1))))
    | ~ linordered_semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3335]) ).

cnf(c_0_3335_1,axiom,
    ( ~ linordered_semidom(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),one_one(X1)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3335]) ).

cnf(c_0_3336_0,axiom,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4))
    | ~ comm_semiring_1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3336]) ).

cnf(c_0_3336_1,axiom,
    ( ~ comm_semiring_1(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3336]) ).

cnf(c_0_3337_0,axiom,
    ( hBOOL(hAPP(nat,bool,X3,X1))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,X3,X2))
    | ~ hBOOL(hAPP(nat,bool,X3,sk1_esk86_3(X3,X1,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_3337]) ).

cnf(c_0_3337_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,X3,X1))
    | ~ hBOOL(hAPP(nat,bool,X3,X2))
    | ~ hBOOL(hAPP(nat,bool,X3,sk1_esk86_3(X3,X1,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_3337]) ).

cnf(c_0_3337_2,axiom,
    ( ~ hBOOL(hAPP(nat,bool,X3,X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,X3,X1))
    | ~ hBOOL(hAPP(nat,bool,X3,sk1_esk86_3(X3,X1,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_3337]) ).

cnf(c_0_3337_3,axiom,
    ( ~ hBOOL(hAPP(nat,bool,X3,sk1_esk86_3(X3,X1,X2)))
    | ~ hBOOL(hAPP(nat,bool,X3,X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,X3,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_3337]) ).

cnf(c_0_3338_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ dense_linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),sk1_esk37_3(X1,X3,X2)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3338]) ).

cnf(c_0_3338_1,axiom,
    ( ~ dense_linorder(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),sk1_esk37_3(X1,X3,X2)),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3338]) ).

cnf(c_0_3338_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),sk1_esk37_3(X1,X3,X2)),X3))
    | ~ dense_linorder(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3338]) ).

cnf(c_0_3339_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X1,bool),nat,finite_card(X1),X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_3339]) ).

cnf(c_0_3339_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X1,bool),nat,finite_card(X1),X2)))
    | hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3339]) ).

cnf(c_0_3340_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3340]) ).

cnf(c_0_3340_1,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3340]) ).

cnf(c_0_3340_2,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3340]) ).

cnf(c_0_3341_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3341]) ).

cnf(c_0_3341_1,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3))
    | hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3341]) ).

cnf(c_0_3341_2,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3))
    | hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3341]) ).

cnf(c_0_3344_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | X1 = X2
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_3344]) ).

cnf(c_0_3344_1,axiom,
    ( X1 = X2
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_3344]) ).

cnf(c_0_3344_2,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
    | X1 = X2
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_3344]) ).

cnf(c_0_3344_3,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),X3,X2),X1))
    | X1 = X2
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3344]) ).

cnf(c_0_3346_0,axiom,
    ( hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,X1),X2))
    | hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,sk1_esk32_2(X1,X2)) != hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),sk1_esk32_2(X1,X2),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3346]) ).

cnf(c_0_3346_1,axiom,
    ( hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),X1,sk1_esk32_2(X1,X2)) != hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),sk1_esk32_2(X1,X2),X2)
    | hBOOL(hAPP(arrow_660593299e_indi,bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool),arrow_218898985ctator,X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3346]) ).

cnf(c_0_3347_0,axiom,
    ( hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
    | ~ hBOOL(hAPP(nat,bool,X1,X2))
    | ~ hBOOL(hAPP(nat,bool,X1,X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),sk1_esk81_2(X2,X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_3347]) ).

cnf(c_0_3347_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,X1,X2))
    | hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
    | ~ hBOOL(hAPP(nat,bool,X1,X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),sk1_esk81_2(X2,X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_3347]) ).

cnf(c_0_3347_2,axiom,
    ( ~ hBOOL(hAPP(nat,bool,X1,X3))
    | ~ hBOOL(hAPP(nat,bool,X1,X2))
    | hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),sk1_esk81_2(X2,X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_3347]) ).

cnf(c_0_3347_3,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X3),sk1_esk81_2(X2,X1)))
    | ~ hBOOL(hAPP(nat,bool,X1,X3))
    | ~ hBOOL(hAPP(nat,bool,X1,X2))
    | hBOOL(hAPP(nat,bool,X1,zero_zero(nat))) ),
    inference(literals_permutation,[status(thm)],[c_0_3347]) ).

cnf(c_0_3348_0,axiom,
    ( hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
    | ~ hBOOL(hAPP(nat,bool,X1,X2))
    | ~ hBOOL(hAPP(nat,bool,X1,X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),sk1_esk79_2(X2,X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_3348]) ).

cnf(c_0_3348_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,X1,X2))
    | hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
    | ~ hBOOL(hAPP(nat,bool,X1,X3))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),sk1_esk79_2(X2,X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_3348]) ).

cnf(c_0_3348_2,axiom,
    ( ~ hBOOL(hAPP(nat,bool,X1,X3))
    | ~ hBOOL(hAPP(nat,bool,X1,X2))
    | hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),sk1_esk79_2(X2,X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_3348]) ).

cnf(c_0_3348_3,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X3),sk1_esk79_2(X2,X1)))
    | ~ hBOOL(hAPP(nat,bool,X1,X3))
    | ~ hBOOL(hAPP(nat,bool,X1,X2))
    | hBOOL(hAPP(nat,bool,X1,zero_zero(nat))) ),
    inference(literals_permutation,[status(thm)],[c_0_3348]) ).

cnf(c_0_3349_0,axiom,
    ( hBOOL(hAPP(X1,bool,X2,X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X2))
    | ~ hBOOL(hAPP(X1,bool,X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3349]) ).

cnf(c_0_3349_1,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X2))
    | hBOOL(hAPP(X1,bool,X2,X3))
    | ~ hBOOL(hAPP(X1,bool,X4,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3349]) ).

cnf(c_0_3349_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,X4,X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X2))
    | hBOOL(hAPP(X1,bool,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3349]) ).

cnf(c_0_3350_0,axiom,
    ( hBOOL(hAPP(X1,bool,X2,X3))
    | ~ hBOOL(hAPP(X1,bool,X4,X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3350]) ).

cnf(c_0_3350_1,axiom,
    ( ~ hBOOL(hAPP(X1,bool,X4,X3))
    | hBOOL(hAPP(X1,bool,X2,X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3350]) ).

cnf(c_0_3350_2,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X4),X2))
    | ~ hBOOL(hAPP(X1,bool,X4,X3))
    | hBOOL(hAPP(X1,bool,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3350]) ).

cnf(c_0_3351_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk72_2(X1,X2)),X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3351]) ).

cnf(c_0_3351_1,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk72_2(X1,X2)),X2))
    | hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3351]) ).

cnf(c_0_3351_2,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk72_2(X1,X2)),X2))
    | hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3351]) ).

cnf(c_0_3352_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | X2 != hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3352]) ).

cnf(c_0_3352_1,axiom,
    ( X2 != hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X3))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3352]) ).

cnf(c_0_3354_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk53_3(X1,X3,X2)),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3354]) ).

cnf(c_0_3354_1,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk53_3(X1,X3,X2)),X2))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3354]) ).

cnf(c_0_3355_0,axiom,
    ( X2 = hAPP(nat,nat,suc,X1)
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),sk1_esk93_2(X1,X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3355]) ).

cnf(c_0_3355_1,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),sk1_esk93_2(X1,X2)))
    | X2 = hAPP(nat,nat,suc,X1)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3355]) ).

cnf(c_0_3355_2,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),sk1_esk93_2(X1,X2)))
    | X2 = hAPP(nat,nat,suc,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3355]) ).

cnf(c_0_3356_0,axiom,
    ( hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),sk1_esk87_2(X2,X1))) = X1
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_3356]) ).

cnf(c_0_3356_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1))
    | hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),sk1_esk87_2(X2,X1))) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_3356]) ).

cnf(c_0_3357_0,axiom,
    ( hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),sk1_esk83_2(X2,X1))) = X1
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_3357]) ).

cnf(c_0_3357_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1))
    | hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),sk1_esk83_2(X2,X1))) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_3357]) ).

cnf(c_0_3358_0,axiom,
    ( X1 = zero_zero(nat)
    | hAPP(nat,nat,suc,sk1_esk85_2(X1,X2)) = X1
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_3358]) ).

cnf(c_0_3358_1,axiom,
    ( hAPP(nat,nat,suc,sk1_esk85_2(X1,X2)) = X1
    | X1 = zero_zero(nat)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_3358]) ).

cnf(c_0_3358_2,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2)))
    | hAPP(nat,nat,suc,sk1_esk85_2(X1,X2)) = X1
    | X1 = zero_zero(nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3358]) ).

cnf(c_0_3359_0,axiom,
    ( ti(X1,X2) = zero_zero(X1)
    | ~ ring_char_0(X1)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),ring_1_Ints(X1)))
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2) != zero_zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3359]) ).

cnf(c_0_3359_1,axiom,
    ( ~ ring_char_0(X1)
    | ti(X1,X2) = zero_zero(X1)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),ring_1_Ints(X1)))
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2) != zero_zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3359]) ).

cnf(c_0_3359_2,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),ring_1_Ints(X1)))
    | ~ ring_char_0(X1)
    | ti(X1,X2) = zero_zero(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2) != zero_zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3359]) ).

cnf(c_0_3359_3,axiom,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2) != zero_zero(X1)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),ring_1_Ints(X1)))
    | ~ ring_char_0(X1)
    | ti(X1,X2) = zero_zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3359]) ).

cnf(c_0_3360_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ti(X1,X3) != ti(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3360]) ).

cnf(c_0_3360_1,axiom,
    ( ~ order(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ti(X1,X3) != ti(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3360]) ).

cnf(c_0_3360_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ order(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ti(X1,X3) != ti(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3360]) ).

cnf(c_0_3360_3,axiom,
    ( ti(X1,X3) != ti(X1,X2)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ order(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3360]) ).

cnf(c_0_3361_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | ti(X1,X3) != ti(X1,X4)
    | ~ order(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3361]) ).

cnf(c_0_3361_1,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ti(X1,X3) != ti(X1,X4)
    | ~ order(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3361]) ).

cnf(c_0_3361_2,axiom,
    ( ti(X1,X3) != ti(X1,X4)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ order(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3361]) ).

cnf(c_0_3361_3,axiom,
    ( ~ order(X1)
    | ti(X1,X3) != ti(X1,X4)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3361]) ).

cnf(c_0_3362_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ti(X1,X4) != ti(X1,X2)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
    | ~ order(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3362]) ).

cnf(c_0_3362_1,axiom,
    ( ti(X1,X4) != ti(X1,X2)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
    | ~ order(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3362]) ).

cnf(c_0_3362_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
    | ti(X1,X4) != ti(X1,X2)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ order(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3362]) ).

cnf(c_0_3362_3,axiom,
    ( ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
    | ti(X1,X4) != ti(X1,X2)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3362]) ).

cnf(c_0_3363_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ti(X1,X3) != ti(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3363]) ).

cnf(c_0_3363_1,axiom,
    ( ~ linorder(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ti(X1,X3) != ti(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3363]) ).

cnf(c_0_3363_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ linorder(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X3) != ti(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3363]) ).

cnf(c_0_3363_3,axiom,
    ( ti(X1,X3) != ti(X1,X2)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ linorder(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3363]) ).

cnf(c_0_3364_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | ti(X1,X3) != ti(X1,X4)
    | ~ order(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3364]) ).

cnf(c_0_3364_1,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X3) != ti(X1,X4)
    | ~ order(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3364]) ).

cnf(c_0_3364_2,axiom,
    ( ti(X1,X3) != ti(X1,X4)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ order(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3364]) ).

cnf(c_0_3364_3,axiom,
    ( ~ order(X1)
    | ti(X1,X3) != ti(X1,X4)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3364]) ).

cnf(c_0_3365_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X4) != ti(X1,X2)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
    | ~ order(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3365]) ).

cnf(c_0_3365_1,axiom,
    ( ti(X1,X4) != ti(X1,X2)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
    | ~ order(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3365]) ).

cnf(c_0_3365_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
    | ti(X1,X4) != ti(X1,X2)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ order(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3365]) ).

cnf(c_0_3365_3,axiom,
    ( ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
    | ti(X1,X4) != ti(X1,X2)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3365]) ).

cnf(c_0_3366_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X3) = ti(X1,X2)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ order(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3366]) ).

cnf(c_0_3366_1,axiom,
    ( ti(X1,X3) = ti(X1,X2)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ order(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3366]) ).

cnf(c_0_3366_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ti(X1,X3) = ti(X1,X2)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ order(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3366]) ).

cnf(c_0_3366_3,axiom,
    ( ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ti(X1,X3) = ti(X1,X2)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3366]) ).

cnf(c_0_3367_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X2) = ti(X1,X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ order(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3367]) ).

cnf(c_0_3367_1,axiom,
    ( ti(X1,X2) = ti(X1,X3)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ order(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3367]) ).

cnf(c_0_3367_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ti(X1,X2) = ti(X1,X3)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ order(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3367]) ).

cnf(c_0_3367_3,axiom,
    ( ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ti(X1,X2) = ti(X1,X3)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3367]) ).

cnf(c_0_3368_0,axiom,
    ( ti(X1,X2) = ti(X1,X3)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ order(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3368]) ).

cnf(c_0_3368_1,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X2) = ti(X1,X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ order(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3368]) ).

cnf(c_0_3368_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X2) = ti(X1,X3)
    | ~ order(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3368]) ).

cnf(c_0_3368_3,axiom,
    ( ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X2) = ti(X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3368]) ).

cnf(c_0_3369_0,axiom,
    ( ti(X1,X2) = ti(X1,X3)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3369]) ).

cnf(c_0_3369_1,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X2) = ti(X1,X3)
    | ~ linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3369]) ).

cnf(c_0_3369_2,axiom,
    ( ~ linorder(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X2) = ti(X1,X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3369]) ).

cnf(c_0_3369_3,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ linorder(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X2) = ti(X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3369]) ).

cnf(c_0_3370_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X3) = ti(X1,X2)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ order(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3370]) ).

cnf(c_0_3370_1,axiom,
    ( ti(X1,X3) = ti(X1,X2)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ order(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3370]) ).

cnf(c_0_3370_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ti(X1,X3) = ti(X1,X2)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ order(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3370]) ).

cnf(c_0_3370_3,axiom,
    ( ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ti(X1,X3) = ti(X1,X2)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3370]) ).

cnf(c_0_3371_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X2) = ti(X1,X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ order(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3371]) ).

cnf(c_0_3371_1,axiom,
    ( ti(X1,X2) = ti(X1,X3)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ order(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3371]) ).

cnf(c_0_3371_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ti(X1,X2) = ti(X1,X3)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ order(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3371]) ).

cnf(c_0_3371_3,axiom,
    ( ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ti(X1,X2) = ti(X1,X3)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3371]) ).

cnf(c_0_3372_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X2) = ti(X1,X3)
    | ~ linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3372]) ).

cnf(c_0_3372_1,axiom,
    ( ti(X1,X2) = ti(X1,X3)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3372]) ).

cnf(c_0_3372_2,axiom,
    ( ~ linorder(X1)
    | ti(X1,X2) = ti(X1,X3)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3372]) ).

cnf(c_0_3372_3,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ linorder(X1)
    | ti(X1,X2) = ti(X1,X3)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3372]) ).

cnf(c_0_3373_0,axiom,
    ( ti(X1,X2) = ti(X1,X3)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3373]) ).

cnf(c_0_3373_1,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X2) = ti(X1,X3)
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3373]) ).

cnf(c_0_3373_2,axiom,
    ( ~ order(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X2) = ti(X1,X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3373]) ).

cnf(c_0_3373_3,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ order(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X2) = ti(X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3373]) ).

cnf(c_0_3374_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X2) = ti(X1,X3)
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3374]) ).

cnf(c_0_3374_1,axiom,
    ( ti(X1,X2) = ti(X1,X3)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3374]) ).

cnf(c_0_3374_2,axiom,
    ( ~ order(X1)
    | ti(X1,X2) = ti(X1,X3)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3374]) ).

cnf(c_0_3374_3,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ order(X1)
    | ti(X1,X2) = ti(X1,X3)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3374]) ).

cnf(c_0_3375_0,axiom,
    ( ti(X1,X2) = ti(X1,X3)
    | hAPP(X1,X4,X5,X2) != hAPP(X1,X4,X5,X3)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X4),fun(fun(X1,bool),bool),inj_on(X1,X4),X5),top_top(fun(X1,bool)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3375]) ).

cnf(c_0_3375_1,axiom,
    ( hAPP(X1,X4,X5,X2) != hAPP(X1,X4,X5,X3)
    | ti(X1,X2) = ti(X1,X3)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X4),fun(fun(X1,bool),bool),inj_on(X1,X4),X5),top_top(fun(X1,bool)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3375]) ).

cnf(c_0_3375_2,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X4),fun(fun(X1,bool),bool),inj_on(X1,X4),X5),top_top(fun(X1,bool))))
    | hAPP(X1,X4,X5,X2) != hAPP(X1,X4,X5,X3)
    | ti(X1,X2) = ti(X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3375]) ).

cnf(c_0_3376_0,axiom,
    ( ti(X1,X4) = ti(X1,X5)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),top_top(fun(X1,bool))))
    | hAPP(X1,X2,X3,X4) != hAPP(X1,X2,X3,X5) ),
    inference(literals_permutation,[status(thm)],[c_0_3376]) ).

cnf(c_0_3376_1,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),top_top(fun(X1,bool))))
    | ti(X1,X4) = ti(X1,X5)
    | hAPP(X1,X2,X3,X4) != hAPP(X1,X2,X3,X5) ),
    inference(literals_permutation,[status(thm)],[c_0_3376]) ).

cnf(c_0_3376_2,axiom,
    ( hAPP(X1,X2,X3,X4) != hAPP(X1,X2,X3,X5)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),top_top(fun(X1,bool))))
    | ti(X1,X4) = ti(X1,X5) ),
    inference(literals_permutation,[status(thm)],[c_0_3376]) ).

cnf(c_0_3377_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
    | X2 != X4
    | ~ ord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3377]) ).

cnf(c_0_3377_1,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | X2 != X4
    | ~ ord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3377]) ).

cnf(c_0_3377_2,axiom,
    ( X2 != X4
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ ord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3377]) ).

cnf(c_0_3377_3,axiom,
    ( ~ ord(X1)
    | X2 != X4
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X4),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3377]) ).

cnf(c_0_3378_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | X4 != X3
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | ~ ord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3378]) ).

cnf(c_0_3378_1,axiom,
    ( X4 != X3
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | ~ ord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3378]) ).

cnf(c_0_3378_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | X4 != X3
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ ord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3378]) ).

cnf(c_0_3378_3,axiom,
    ( ~ ord(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X4))
    | X4 != X3
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3378]) ).

cnf(c_0_3379_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
    | X2 != X4
    | ~ ord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3379]) ).

cnf(c_0_3379_1,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | X2 != X4
    | ~ ord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3379]) ).

cnf(c_0_3379_2,axiom,
    ( X2 != X4
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ ord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3379]) ).

cnf(c_0_3379_3,axiom,
    ( ~ ord(X1)
    | X2 != X4
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X4),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3379]) ).

cnf(c_0_3380_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | X4 != X3
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | ~ ord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3380]) ).

cnf(c_0_3380_1,axiom,
    ( X4 != X3
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | ~ ord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3380]) ).

cnf(c_0_3380_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | X4 != X3
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ ord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3380]) ).

cnf(c_0_3380_3,axiom,
    ( ~ ord(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X4))
    | X4 != X3
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3380]) ).

cnf(c_0_3381_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ preorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3381]) ).

cnf(c_0_3381_1,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ preorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3381]) ).

cnf(c_0_3381_2,axiom,
    ( ~ preorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3381]) ).

cnf(c_0_3382_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3382]) ).

cnf(c_0_3382_1,axiom,
    ( ~ order(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3382]) ).

cnf(c_0_3382_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ order(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3382]) ).

cnf(c_0_3383_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ preorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3383]) ).

cnf(c_0_3383_1,axiom,
    ( ~ preorder(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3383]) ).

cnf(c_0_3383_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ preorder(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3383]) ).

cnf(c_0_3384_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3384]) ).

cnf(c_0_3384_1,axiom,
    ( ~ order(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3384]) ).

cnf(c_0_3384_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ order(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3384]) ).

cnf(c_0_3385_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2)))
    | X1 != X2 ),
    inference(literals_permutation,[status(thm)],[c_0_3385]) ).

cnf(c_0_3385_1,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | X1 != X2 ),
    inference(literals_permutation,[status(thm)],[c_0_3385]) ).

cnf(c_0_3385_2,axiom,
    ( X1 != X2
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3385]) ).

cnf(c_0_3386_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_3386]) ).

cnf(c_0_3386_1,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_3386]) ).

cnf(c_0_3388_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),sk1_esk82_2(X1,X2)))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3388]) ).

cnf(c_0_3388_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),sk1_esk82_2(X1,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_3388]) ).

cnf(c_0_3390_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | X1 = X2
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3390]) ).

cnf(c_0_3390_1,axiom,
    ( X1 = X2
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3390]) ).

cnf(c_0_3390_2,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | X1 = X2
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3390]) ).

cnf(c_0_3391_0,axiom,
    ( X1 = X2
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3391]) ).

cnf(c_0_3391_1,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | X1 = X2
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3391]) ).

cnf(c_0_3391_2,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_3391]) ).

cnf(c_0_3392_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | X1 = X2
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3392]) ).

cnf(c_0_3392_1,axiom,
    ( X1 = X2
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3392]) ).

cnf(c_0_3392_2,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | X1 = X2
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3392]) ).

cnf(c_0_3393_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3393]) ).

cnf(c_0_3393_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3393]) ).

cnf(c_0_3394_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3394]) ).

cnf(c_0_3394_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3394]) ).

cnf(c_0_3395_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3395]) ).

cnf(c_0_3395_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3395]) ).

cnf(c_0_3396_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3396]) ).

cnf(c_0_3396_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3396]) ).

cnf(c_0_3397_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3397]) ).

cnf(c_0_3397_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3397]) ).

cnf(c_0_3398_0,axiom,
    ( X1 = zero_zero(nat)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,zero_zero(nat)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3398]) ).

cnf(c_0_3398_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,zero_zero(nat))))
    | X1 = zero_zero(nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3398]) ).

cnf(c_0_3399_0,axiom,
    ( ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2)
    | hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),sk1_esk26_2(X1,X2)),arrow_2064824852le_Lin)) ),
    inference(literals_permutation,[status(thm)],[c_0_3399]) ).

cnf(c_0_3399_1,axiom,
    ( hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),sk1_esk26_2(X1,X2)),arrow_2064824852le_Lin))
    | ti(arrow_490897120le_alt,X1) = ti(arrow_490897120le_alt,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3399]) ).

cnf(c_0_3400_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X1,bool),nat,finite_card(X1),top_top(fun(X1,bool)))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3400]) ).

cnf(c_0_3400_1,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool))))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X1,bool),nat,finite_card(X1),top_top(fun(X1,bool))))) ),
    inference(literals_permutation,[status(thm)],[c_0_3400]) ).

cnf(c_0_3401_0,axiom,
    ( hAPP(X1,X2,X3,X4) = hAPP(X1,X2,X3,X5)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),top_top(fun(X1,bool))))
    | ti(X1,X4) != ti(X1,X5) ),
    inference(literals_permutation,[status(thm)],[c_0_3401]) ).

cnf(c_0_3401_1,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),top_top(fun(X1,bool))))
    | hAPP(X1,X2,X3,X4) = hAPP(X1,X2,X3,X5)
    | ti(X1,X4) != ti(X1,X5) ),
    inference(literals_permutation,[status(thm)],[c_0_3401]) ).

cnf(c_0_3401_2,axiom,
    ( ti(X1,X4) != ti(X1,X5)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),top_top(fun(X1,bool))))
    | hAPP(X1,X2,X3,X4) = hAPP(X1,X2,X3,X5) ),
    inference(literals_permutation,[status(thm)],[c_0_3401]) ).

cnf(c_0_3407_0,axiom,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2) = zero_zero(X1)
    | ~ ring_char_0(X1)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),ring_1_Ints(X1)))
    | ti(X1,X2) != zero_zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3407]) ).

cnf(c_0_3407_1,axiom,
    ( ~ ring_char_0(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2) = zero_zero(X1)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),ring_1_Ints(X1)))
    | ti(X1,X2) != zero_zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3407]) ).

cnf(c_0_3407_2,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),ring_1_Ints(X1)))
    | ~ ring_char_0(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2) = zero_zero(X1)
    | ti(X1,X2) != zero_zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3407]) ).

cnf(c_0_3407_3,axiom,
    ( ti(X1,X2) != zero_zero(X1)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),ring_1_Ints(X1)))
    | ~ ring_char_0(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2) = zero_zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3407]) ).

cnf(c_0_3408_0,axiom,
    ( hBOOL(hAPP(nat,bool,X1,X2))
    | ~ hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
    | ~ hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,suc,sk1_esk98_2(X2,X1)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3408]) ).

cnf(c_0_3408_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
    | hBOOL(hAPP(nat,bool,X1,X2))
    | ~ hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,suc,sk1_esk98_2(X2,X1)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3408]) ).

cnf(c_0_3408_2,axiom,
    ( ~ hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,suc,sk1_esk98_2(X2,X1))))
    | ~ hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
    | hBOOL(hAPP(nat,bool,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3408]) ).

cnf(c_0_3409_0,axiom,
    ( hAPP(fun(sum_sum(X1,X2),bool),nat,finite_card(sum_sum(X1,X2)),hAPP(fun(X2,bool),fun(sum_sum(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X2,bool),fun(sum_sum(X1,X2),bool)),sum_Plus(X1,X2),X3),X4)) = zero_zero(nat)
    | hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3409]) ).

cnf(c_0_3409_1,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X3))
    | hAPP(fun(sum_sum(X1,X2),bool),nat,finite_card(sum_sum(X1,X2)),hAPP(fun(X2,bool),fun(sum_sum(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X2,bool),fun(sum_sum(X1,X2),bool)),sum_Plus(X1,X2),X3),X4)) = zero_zero(nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3409]) ).

cnf(c_0_3410_0,axiom,
    ( hAPP(fun(sum_sum(X1,X2),bool),nat,finite_card(sum_sum(X1,X2)),hAPP(fun(X2,bool),fun(sum_sum(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X2,bool),fun(sum_sum(X1,X2),bool)),sum_Plus(X1,X2),X3),X4)) = zero_zero(nat)
    | hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3410]) ).

cnf(c_0_3410_1,axiom,
    ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),X4))
    | hAPP(fun(sum_sum(X1,X2),bool),nat,finite_card(sum_sum(X1,X2)),hAPP(fun(X2,bool),fun(sum_sum(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X2,bool),fun(sum_sum(X1,X2),bool)),sum_Plus(X1,X2),X3),X4)) = zero_zero(nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3410]) ).

cnf(c_0_3411_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),sk1_esk37_3(X1,X3,X2)),X2))
    | ~ dense_linorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3411]) ).

cnf(c_0_3411_1,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),sk1_esk37_3(X1,X3,X2)),X2))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ dense_linorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3411]) ).

cnf(c_0_3411_2,axiom,
    ( ~ dense_linorder(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),sk1_esk37_3(X1,X3,X2)),X2))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3411]) ).

cnf(c_0_3414_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | ti(X1,sk1_esk70_4(X2,X1,X3,X4)) != ti(X1,sk1_esk69_4(X2,X1,X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3414]) ).

cnf(c_0_3414_1,axiom,
    ( ti(X1,sk1_esk70_4(X2,X1,X3,X4)) != ti(X1,sk1_esk69_4(X2,X1,X3,X4))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3414]) ).

cnf(c_0_3415_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | ti(X1,sk1_esk31_4(X1,X2,X3,X4)) != ti(X1,sk1_esk30_4(X1,X2,X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3415]) ).

cnf(c_0_3415_1,axiom,
    ( ti(X1,sk1_esk31_4(X1,X2,X3,X4)) != ti(X1,sk1_esk30_4(X1,X2,X3,X4))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3415]) ).

cnf(c_0_3417_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | hAPP(X1,X2,X3,sk1_esk70_4(X2,X1,X3,X4)) = hAPP(X1,X2,X3,sk1_esk69_4(X2,X1,X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3417]) ).

cnf(c_0_3417_1,axiom,
    ( hAPP(X1,X2,X3,sk1_esk70_4(X2,X1,X3,X4)) = hAPP(X1,X2,X3,sk1_esk69_4(X2,X1,X3,X4))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3417]) ).

cnf(c_0_3418_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4))
    | hAPP(X1,X2,X3,sk1_esk31_4(X1,X2,X3,X4)) = hAPP(X1,X2,X3,sk1_esk30_4(X1,X2,X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3418]) ).

cnf(c_0_3418_1,axiom,
    ( hAPP(X1,X2,X3,sk1_esk31_4(X1,X2,X3,X4)) = hAPP(X1,X2,X3,sk1_esk30_4(X1,X2,X3,X4))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3418]) ).

cnf(c_0_3419_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),sk1_esk99_3(X1,X2,X3)))
    | ~ linordered_field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3419]) ).

cnf(c_0_3419_1,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),sk1_esk99_3(X1,X2,X3)))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ linordered_field(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3419]) ).

cnf(c_0_3419_2,axiom,
    ( ~ linordered_field(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),sk1_esk99_3(X1,X2,X3)))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3419]) ).

cnf(c_0_3420_0,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3))
    | ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3420]) ).

cnf(c_0_3420_1,axiom,
    ( ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less(fun(X1,bool)),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3420]) ).

cnf(c_0_3421_0,axiom,
    ( hBOOL(hAPP(X1,bool,X2,X3))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3421]) ).

cnf(c_0_3421_1,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X3),X2))
    | hBOOL(hAPP(X1,bool,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3421]) ).

cnf(c_0_3422_0,axiom,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),sk1_esk82_2(X1,X2)) = X2
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3422]) ).

cnf(c_0_3422_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),sk1_esk82_2(X1,X2)) = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_3422]) ).

cnf(c_0_3423_0,axiom,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),sk1_esk60_2(X2,X1)) = X1
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_3423]) ).

cnf(c_0_3423_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1))
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),sk1_esk60_2(X2,X1)) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_3423]) ).

cnf(c_0_3424_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ linorder(X1)
    | ti(X1,X2) != ti(X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3424]) ).

cnf(c_0_3424_1,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ linorder(X1)
    | ti(X1,X2) != ti(X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3424]) ).

cnf(c_0_3424_2,axiom,
    ( ~ linorder(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X2) != ti(X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3424]) ).

cnf(c_0_3424_3,axiom,
    ( ti(X1,X2) != ti(X1,X3)
    | ~ linorder(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3424]) ).

cnf(c_0_3425_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ti(X1,X3) = ti(X1,X2)
    | ~ linordered_idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3425]) ).

cnf(c_0_3425_1,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X3) = ti(X1,X2)
    | ~ linordered_idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3425]) ).

cnf(c_0_3425_2,axiom,
    ( ti(X1,X3) = ti(X1,X2)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ linordered_idom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3425]) ).

cnf(c_0_3425_3,axiom,
    ( ~ linordered_idom(X1)
    | ti(X1,X3) = ti(X1,X2)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3425]) ).

cnf(c_0_3426_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ti(X1,X3) = ti(X1,X2)
    | ~ linorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3426]) ).

cnf(c_0_3426_1,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X3) = ti(X1,X2)
    | ~ linorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3426]) ).

cnf(c_0_3426_2,axiom,
    ( ti(X1,X3) = ti(X1,X2)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ linorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3426]) ).

cnf(c_0_3426_3,axiom,
    ( ~ linorder(X1)
    | ti(X1,X3) = ti(X1,X2)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3426]) ).

cnf(c_0_3427_0,axiom,
    ( ti(X1,X2) = ti(X1,X3)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ linorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3427]) ).

cnf(c_0_3427_1,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ti(X1,X2) = ti(X1,X3)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ linorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3427]) ).

cnf(c_0_3427_2,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ti(X1,X2) = ti(X1,X3)
    | ~ linorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3427]) ).

cnf(c_0_3427_3,axiom,
    ( ~ linorder(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ti(X1,X2) = ti(X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3427]) ).

cnf(c_0_3428_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X3) = ti(X1,X2)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ linorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3428]) ).

cnf(c_0_3428_1,axiom,
    ( ti(X1,X3) = ti(X1,X2)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ linorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3428]) ).

cnf(c_0_3428_2,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ti(X1,X3) = ti(X1,X2)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ linorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3428]) ).

cnf(c_0_3428_3,axiom,
    ( ~ linorder(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ti(X1,X3) = ti(X1,X2)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3428]) ).

cnf(c_0_3429_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X3) = ti(X1,X2)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ linorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3429]) ).

cnf(c_0_3429_1,axiom,
    ( ti(X1,X3) = ti(X1,X2)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ linorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3429]) ).

cnf(c_0_3429_2,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ti(X1,X3) = ti(X1,X2)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ linorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3429]) ).

cnf(c_0_3429_3,axiom,
    ( ~ linorder(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ti(X1,X3) = ti(X1,X2)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3429]) ).

cnf(c_0_3430_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ti(X1,X3) = ti(X1,X2)
    | ~ linorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3430]) ).

cnf(c_0_3430_1,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X3) = ti(X1,X2)
    | ~ linorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3430]) ).

cnf(c_0_3430_2,axiom,
    ( ti(X1,X3) = ti(X1,X2)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ linorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3430]) ).

cnf(c_0_3430_3,axiom,
    ( ~ linorder(X1)
    | ti(X1,X3) = ti(X1,X2)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3430]) ).

cnf(c_0_3431_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X3) = ti(X1,X2)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ linorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3431]) ).

cnf(c_0_3431_1,axiom,
    ( ti(X1,X3) = ti(X1,X2)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ linorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3431]) ).

cnf(c_0_3431_2,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ti(X1,X3) = ti(X1,X2)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ linorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3431]) ).

cnf(c_0_3431_3,axiom,
    ( ~ linorder(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ti(X1,X3) = ti(X1,X2)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3431]) ).

cnf(c_0_3432_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ linorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3432]) ).

cnf(c_0_3432_1,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ linorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3432]) ).

cnf(c_0_3432_2,axiom,
    ( ~ linorder(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3432]) ).

cnf(c_0_3433_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ linorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3433]) ).

cnf(c_0_3433_1,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ linorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3433]) ).

cnf(c_0_3433_2,axiom,
    ( ~ linorder(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3433]) ).

cnf(c_0_3434_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ linorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3434]) ).

cnf(c_0_3434_1,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ linorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3434]) ).

cnf(c_0_3434_2,axiom,
    ( ~ linorder(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3434]) ).

cnf(c_0_3435_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ linorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3435]) ).

cnf(c_0_3435_1,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ linorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3435]) ).

cnf(c_0_3435_2,axiom,
    ( ~ linorder(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3435]) ).

cnf(c_0_3436_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ linorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3436]) ).

cnf(c_0_3436_1,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ linorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3436]) ).

cnf(c_0_3436_2,axiom,
    ( ~ linorder(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3436]) ).

cnf(c_0_3437_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ linorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3437]) ).

cnf(c_0_3437_1,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ linorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3437]) ).

cnf(c_0_3437_2,axiom,
    ( ~ linorder(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3437]) ).

cnf(c_0_3438_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ linorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3438]) ).

cnf(c_0_3438_1,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ linorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3438]) ).

cnf(c_0_3438_2,axiom,
    ( ~ linorder(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3438]) ).

cnf(c_0_3439_0,axiom,
    ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X1))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sk1_esk78_2(X2,X1)),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3439]) ).

cnf(c_0_3439_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sk1_esk78_2(X2,X1)),X2))
    | hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_3439]) ).

cnf(c_0_3440_0,axiom,
    ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X1))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sk1_esk76_2(X1,X2)),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3440]) ).

cnf(c_0_3440_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sk1_esk76_2(X1,X2)),X2))
    | hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_3440]) ).

cnf(c_0_3441_0,axiom,
    ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X1))
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sk1_esk74_2(X1,X2)),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3441]) ).

cnf(c_0_3441_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sk1_esk74_2(X1,X2)),X2))
    | hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_3441]) ).

cnf(c_0_3442_0,axiom,
    ( hBOOL(hAPP(fun(sum_sum(X1,X2),bool),bool,finite_finite_1(sum_sum(X1,X2)),top_top(fun(sum_sum(X1,X2),bool))))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),top_top(fun(X2,bool))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3442]) ).

cnf(c_0_3442_1,axiom,
    ( ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),top_top(fun(X2,bool))))
    | hBOOL(hAPP(fun(sum_sum(X1,X2),bool),bool,finite_finite_1(sum_sum(X1,X2)),top_top(fun(sum_sum(X1,X2),bool))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3442]) ).

cnf(c_0_3442_2,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool))))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),top_top(fun(X2,bool))))
    | hBOOL(hAPP(fun(sum_sum(X1,X2),bool),bool,finite_finite_1(sum_sum(X1,X2)),top_top(fun(sum_sum(X1,X2),bool)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3442]) ).

cnf(c_0_3443_0,axiom,
    ( hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,finite_finite_1(product_prod(X1,X2)),top_top(fun(product_prod(X1,X2),bool))))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),top_top(fun(X2,bool))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3443]) ).

cnf(c_0_3443_1,axiom,
    ( ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),top_top(fun(X2,bool))))
    | hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,finite_finite_1(product_prod(X1,X2)),top_top(fun(product_prod(X1,X2),bool))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3443]) ).

cnf(c_0_3443_2,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool))))
    | ~ hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),top_top(fun(X2,bool))))
    | hBOOL(hAPP(fun(product_prod(X1,X2),bool),bool,finite_finite_1(product_prod(X1,X2)),top_top(fun(product_prod(X1,X2),bool)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3443]) ).

cnf(c_0_3444_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1))
    | X2 = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_3444]) ).

cnf(c_0_3444_1,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | X2 = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_3444]) ).

cnf(c_0_3444_2,axiom,
    ( X2 = X1
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3444]) ).

cnf(c_0_3445_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1))
    | X2 = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_3445]) ).

cnf(c_0_3445_1,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | X2 = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_3445]) ).

cnf(c_0_3445_2,axiom,
    ( X2 = X1
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3445]) ).

cnf(c_0_3446_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_3446]) ).

cnf(c_0_3446_1,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X2),X1))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3446]) ).

cnf(c_0_3447_0,axiom,
    ( ti(X2,X3) = ti(X2,X5)
    | hAPP(X1,product_prod(X2,X1),hAPP(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),X3),X4) != hAPP(X1,product_prod(X2,X1),hAPP(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),X5),X6) ),
    inference(literals_permutation,[status(thm)],[c_0_3447]) ).

cnf(c_0_3447_1,axiom,
    ( hAPP(X1,product_prod(X2,X1),hAPP(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),X3),X4) != hAPP(X1,product_prod(X2,X1),hAPP(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),X5),X6)
    | ti(X2,X3) = ti(X2,X5) ),
    inference(literals_permutation,[status(thm)],[c_0_3447]) ).

cnf(c_0_3448_0,axiom,
    ( ti(X1,X4) = ti(X1,X6)
    | hAPP(X1,product_prod(X2,X1),hAPP(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),X3),X4) != hAPP(X1,product_prod(X2,X1),hAPP(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),X5),X6) ),
    inference(literals_permutation,[status(thm)],[c_0_3448]) ).

cnf(c_0_3448_1,axiom,
    ( hAPP(X1,product_prod(X2,X1),hAPP(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),X3),X4) != hAPP(X1,product_prod(X2,X1),hAPP(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),X5),X6)
    | ti(X1,X4) = ti(X1,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_3448]) ).

cnf(c_0_3449_0,axiom,
    ( ti(X2,X3) = ti(X2,X5)
    | hAPP(X1,product_prod(X2,X1),hAPP(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),X3),X4) != hAPP(X1,product_prod(X2,X1),hAPP(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),X5),X6) ),
    inference(literals_permutation,[status(thm)],[c_0_3449]) ).

cnf(c_0_3449_1,axiom,
    ( hAPP(X1,product_prod(X2,X1),hAPP(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),X3),X4) != hAPP(X1,product_prod(X2,X1),hAPP(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),X5),X6)
    | ti(X2,X3) = ti(X2,X5) ),
    inference(literals_permutation,[status(thm)],[c_0_3449]) ).

cnf(c_0_3450_0,axiom,
    ( ti(X1,X4) = ti(X1,X6)
    | hAPP(X1,product_prod(X2,X1),hAPP(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),X3),X4) != hAPP(X1,product_prod(X2,X1),hAPP(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),X5),X6) ),
    inference(literals_permutation,[status(thm)],[c_0_3450]) ).

cnf(c_0_3450_1,axiom,
    ( hAPP(X1,product_prod(X2,X1),hAPP(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),X3),X4) != hAPP(X1,product_prod(X2,X1),hAPP(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),X5),X6)
    | ti(X1,X4) = ti(X1,X6) ),
    inference(literals_permutation,[status(thm)],[c_0_3450]) ).

cnf(c_0_3451_0,axiom,
    ( hAPP(fun(X1,bool),nat,finite_card(X1),X2) = zero_zero(nat)
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk80_2(X1,X2)),X2))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3451]) ).

cnf(c_0_3451_1,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk80_2(X1,X2)),X2))
    | hAPP(fun(X1,bool),nat,finite_card(X1),X2) = zero_zero(nat)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3451]) ).

cnf(c_0_3451_2,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),sk1_esk80_2(X1,X2)),X2))
    | hAPP(fun(X1,bool),nat,finite_card(X1),X2) = zero_zero(nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3451]) ).

cnf(c_0_3454_0,axiom,
    ( X2 = hAPP(nat,nat,suc,X1)
    | hAPP(nat,nat,suc,sk1_esk93_2(X1,X2)) = X2
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3454]) ).

cnf(c_0_3454_1,axiom,
    ( hAPP(nat,nat,suc,sk1_esk93_2(X1,X2)) = X2
    | X2 = hAPP(nat,nat,suc,X1)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3454]) ).

cnf(c_0_3454_2,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | hAPP(nat,nat,suc,sk1_esk93_2(X1,X2)) = X2
    | X2 = hAPP(nat,nat,suc,X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3454]) ).

cnf(c_0_3455_0,axiom,
    ( hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sk1_esk81_2(X2,X1)),X2))
    | ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3455]) ).

cnf(c_0_3455_1,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sk1_esk81_2(X2,X1)),X2))
    | hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
    | ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3455]) ).

cnf(c_0_3455_2,axiom,
    ( ~ hBOOL(hAPP(nat,bool,X1,X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),sk1_esk81_2(X2,X1)),X2))
    | hBOOL(hAPP(nat,bool,X1,zero_zero(nat))) ),
    inference(literals_permutation,[status(thm)],[c_0_3455]) ).

cnf(c_0_3456_0,axiom,
    ( hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sk1_esk79_2(X2,X1)),X2))
    | ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3456]) ).

cnf(c_0_3456_1,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sk1_esk79_2(X2,X1)),X2))
    | hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
    | ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3456]) ).

cnf(c_0_3456_2,axiom,
    ( ~ hBOOL(hAPP(nat,bool,X1,X2))
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sk1_esk79_2(X2,X1)),X2))
    | hBOOL(hAPP(nat,bool,X1,zero_zero(nat))) ),
    inference(literals_permutation,[status(thm)],[c_0_3456]) ).

cnf(c_0_3457_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,suc,X2)))
    | X1 != hAPP(nat,nat,suc,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3457]) ).

cnf(c_0_3457_1,axiom,
    ( X1 != hAPP(nat,nat,suc,X2)
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,suc,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_3457]) ).

cnf(c_0_3458_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool))))
    | hAPP(fun(X2,bool),nat,finite_card(X2),top_top(fun(X2,bool))) = hAPP(nat,nat,suc,zero_zero(nat))
    | ~ hBOOL(hAPP(fun(fun(X1,X2),bool),bool,finite_finite_1(fun(X1,X2)),top_top(fun(fun(X1,X2),bool)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3458]) ).

cnf(c_0_3458_1,axiom,
    ( hAPP(fun(X2,bool),nat,finite_card(X2),top_top(fun(X2,bool))) = hAPP(nat,nat,suc,zero_zero(nat))
    | hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool))))
    | ~ hBOOL(hAPP(fun(fun(X1,X2),bool),bool,finite_finite_1(fun(X1,X2)),top_top(fun(fun(X1,X2),bool)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3458]) ).

cnf(c_0_3458_2,axiom,
    ( ~ hBOOL(hAPP(fun(fun(X1,X2),bool),bool,finite_finite_1(fun(X1,X2)),top_top(fun(fun(X1,X2),bool))))
    | hAPP(fun(X2,bool),nat,finite_card(X2),top_top(fun(X2,bool))) = hAPP(nat,nat,suc,zero_zero(nat))
    | hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3458]) ).

cnf(c_0_3459_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),top_top(fun(X1,bool))))
    | hAPP(X1,X2,X3,sk1_esk36_3(X1,X2,X3)) = hAPP(X1,X2,X3,sk1_esk35_3(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3459]) ).

cnf(c_0_3459_1,axiom,
    ( hAPP(X1,X2,X3,sk1_esk36_3(X1,X2,X3)) = hAPP(X1,X2,X3,sk1_esk35_3(X1,X2,X3))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),top_top(fun(X1,bool)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3459]) ).

cnf(c_0_3463_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | X2 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3463]) ).

cnf(c_0_3463_1,axiom,
    ( X2 != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X3)
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3463]) ).

cnf(c_0_3464_0,axiom,
    ( hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
    | hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,suc,sk1_esk97_1(X1))))
    | ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3464]) ).

cnf(c_0_3464_1,axiom,
    ( hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,suc,sk1_esk97_1(X1))))
    | hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
    | ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3464]) ).

cnf(c_0_3464_2,axiom,
    ( ~ hBOOL(hAPP(nat,bool,X1,X2))
    | hBOOL(hAPP(nat,bool,X1,hAPP(nat,nat,suc,sk1_esk97_1(X1))))
    | hBOOL(hAPP(nat,bool,X1,zero_zero(nat))) ),
    inference(literals_permutation,[status(thm)],[c_0_3464]) ).

cnf(c_0_3465_0,axiom,
    ( hAPP(nat,nat,suc,sk1_esk88_1(X1)) = X1
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_3465]) ).

cnf(c_0_3465_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
    | hAPP(nat,nat,suc,sk1_esk88_1(X1)) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_3465]) ).

cnf(c_0_3466_0,axiom,
    ( hAPP(nat,nat,suc,sk1_esk84_1(X1)) = X1
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_3466]) ).

cnf(c_0_3466_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
    | hAPP(nat,nat,suc,sk1_esk84_1(X1)) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_3466]) ).

cnf(c_0_3470_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3))
    | ~ hBOOL(hAPP(X1,bool,X3,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3470]) ).

cnf(c_0_3470_1,axiom,
    ( ~ hBOOL(hAPP(X1,bool,X3,X2))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3470]) ).

cnf(c_0_3471_0,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),zero_zero(X1)))
    | ~ linordered_semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3471]) ).

cnf(c_0_3471_1,axiom,
    ( ~ linordered_semidom(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),one_one(X1)),zero_zero(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_3471]) ).

cnf(c_0_3472_0,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),one_one(X1)),zero_zero(X1)))
    | ~ linordered_semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3472]) ).

cnf(c_0_3472_1,axiom,
    ( ~ linordered_semidom(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),one_one(X1)),zero_zero(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_3472]) ).

cnf(c_0_3473_0,axiom,
    ( ti(X1,X2) = top_top(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),top_top(X1)),X2))
    | ~ top(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3473]) ).

cnf(c_0_3473_1,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),top_top(X1)),X2))
    | ti(X1,X2) = top_top(X1)
    | ~ top(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3473]) ).

cnf(c_0_3473_2,axiom,
    ( ~ top(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),top_top(X1)),X2))
    | ti(X1,X2) = top_top(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3473]) ).

cnf(c_0_3474_0,axiom,
    ( ti(X1,X2) = top_top(X1)
    | ~ top(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),top_top(X1)),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3474]) ).

cnf(c_0_3474_1,axiom,
    ( ~ top(X1)
    | ti(X1,X2) = top_top(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),top_top(X1)),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3474]) ).

cnf(c_0_3474_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),top_top(X1)),X2))
    | ~ top(X1)
    | ti(X1,X2) = top_top(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3474]) ).

cnf(c_0_3475_0,axiom,
    ( ti(X1,X2) = ti(X1,X3)
    | ~ cancel_semigroup_add(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X2) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3475]) ).

cnf(c_0_3475_1,axiom,
    ( ~ cancel_semigroup_add(X1)
    | ti(X1,X2) = ti(X1,X3)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X2) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3475]) ).

cnf(c_0_3475_2,axiom,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X2) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)
    | ~ cancel_semigroup_add(X1)
    | ti(X1,X2) = ti(X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3475]) ).

cnf(c_0_3476_0,axiom,
    ( ti(X1,X2) = ti(X1,X3)
    | ~ cancel_semigroup_add(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_3476]) ).

cnf(c_0_3476_1,axiom,
    ( ~ cancel_semigroup_add(X1)
    | ti(X1,X2) = ti(X1,X3)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_3476]) ).

cnf(c_0_3476_2,axiom,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)
    | ~ cancel_semigroup_add(X1)
    | ti(X1,X2) = ti(X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3476]) ).

cnf(c_0_3477_0,axiom,
    ( ti(X1,X2) = ti(X1,X3)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X2) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)
    | ~ cancel_semigroup_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3477]) ).

cnf(c_0_3477_1,axiom,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X2) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)
    | ti(X1,X2) = ti(X1,X3)
    | ~ cancel_semigroup_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3477]) ).

cnf(c_0_3477_2,axiom,
    ( ~ cancel_semigroup_add(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X2) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)
    | ti(X1,X2) = ti(X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3477]) ).

cnf(c_0_3478_0,axiom,
    ( ti(X1,X2) = ti(X1,X3)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X2) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)
    | ~ cancel146912293up_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3478]) ).

cnf(c_0_3478_1,axiom,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X2) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)
    | ti(X1,X2) = ti(X1,X3)
    | ~ cancel146912293up_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3478]) ).

cnf(c_0_3478_2,axiom,
    ( ~ cancel146912293up_add(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X2) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)
    | ti(X1,X2) = ti(X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3478]) ).

cnf(c_0_3479_0,axiom,
    ( ti(X1,X2) = ti(X1,X3)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)
    | ~ cancel_semigroup_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3479]) ).

cnf(c_0_3479_1,axiom,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)
    | ti(X1,X2) = ti(X1,X3)
    | ~ cancel_semigroup_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3479]) ).

cnf(c_0_3479_2,axiom,
    ( ~ cancel_semigroup_add(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4) != hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X4)
    | ti(X1,X2) = ti(X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3479]) ).

cnf(c_0_3480_0,axiom,
    ( ~ top(X1)
    | ti(X1,X2) != top_top(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),top_top(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_3480]) ).

cnf(c_0_3480_1,axiom,
    ( ti(X1,X2) != top_top(X1)
    | ~ top(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),top_top(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_3480]) ).

cnf(c_0_3480_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),top_top(X1)))
    | ti(X1,X2) != top_top(X1)
    | ~ top(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3480]) ).

cnf(c_0_3481_0,axiom,
    ( ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X2) != ti(X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3481]) ).

cnf(c_0_3481_1,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ order(X1)
    | ti(X1,X2) != ti(X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3481]) ).

cnf(c_0_3481_2,axiom,
    ( ti(X1,X2) != ti(X1,X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ order(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3481]) ).

cnf(c_0_3482_0,axiom,
    ( ~ linorder(X1)
    | ti(X1,X2) != ti(X1,X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3482]) ).

cnf(c_0_3482_1,axiom,
    ( ti(X1,X2) != ti(X1,X3)
    | ~ linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3482]) ).

cnf(c_0_3482_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X2) != ti(X1,X3)
    | ~ linorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3482]) ).

cnf(c_0_3483_0,axiom,
    ( ~ linorder(X1)
    | ti(X1,X2) != ti(X1,X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3483]) ).

cnf(c_0_3483_1,axiom,
    ( ti(X1,X2) != ti(X1,X3)
    | ~ linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3483]) ).

cnf(c_0_3483_2,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ti(X1,X2) != ti(X1,X3)
    | ~ linorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3483]) ).

cnf(c_0_3484_0,axiom,
    ( ~ linorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X2) != ti(X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3484]) ).

cnf(c_0_3484_1,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ linorder(X1)
    | ti(X1,X2) != ti(X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3484]) ).

cnf(c_0_3484_2,axiom,
    ( ti(X1,X2) != ti(X1,X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ linorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3484]) ).

cnf(c_0_3485_0,axiom,
    ( ti(X1,X2) != ti(X1,X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ order(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3485]) ).

cnf(c_0_3485_1,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X2) != ti(X1,X3)
    | ~ order(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3485]) ).

cnf(c_0_3485_2,axiom,
    ( ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X2) != ti(X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3485]) ).

cnf(c_0_3486_0,axiom,
    ( ti(X1,X2) != ti(X1,X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ~ order(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3486]) ).

cnf(c_0_3486_1,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X2) != ti(X1,X3)
    | ~ order(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3486]) ).

cnf(c_0_3486_2,axiom,
    ( ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
    | ti(X1,X2) != ti(X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3486]) ).

cnf(c_0_3487_0,axiom,
    ( ti(X1,X2) != ti(X1,X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ~ order(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3487]) ).

cnf(c_0_3487_1,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ti(X1,X2) != ti(X1,X3)
    | ~ order(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3487]) ).

cnf(c_0_3487_2,axiom,
    ( ~ order(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X3),X2))
    | ti(X1,X2) != ti(X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3487]) ).

cnf(c_0_3488_0,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),top_top(X1)),X2))
    | ~ top(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3488]) ).

cnf(c_0_3488_1,axiom,
    ( ~ top(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),top_top(X1)),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3488]) ).

cnf(c_0_3489_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,zero_zero(nat))))
    | X1 != zero_zero(nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3489]) ).

cnf(c_0_3489_1,axiom,
    ( X1 != zero_zero(nat)
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,zero_zero(nat)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3489]) ).

cnf(c_0_3491_0,axiom,
    ( ti(X1,X2) = ti(X1,X3)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),fequal(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3491]) ).

cnf(c_0_3491_1,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),fequal(X1),X2),X3))
    | ti(X1,X2) = ti(X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3491]) ).

cnf(c_0_3492_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2)))
    | X1 != zero_zero(nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3492]) ).

cnf(c_0_3492_1,axiom,
    ( X1 != zero_zero(nat)
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_3492]) ).

cnf(c_0_3493_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2)))
    | X1 != X2 ),
    inference(literals_permutation,[status(thm)],[c_0_3493]) ).

cnf(c_0_3493_1,axiom,
    ( X1 != X2
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X2))) ),
    inference(literals_permutation,[status(thm)],[c_0_3493]) ).

cnf(c_0_3495_0,axiom,
    ( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X2))
    | ~ preorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3495]) ).

cnf(c_0_3495_1,axiom,
    ( ~ preorder(X1)
    | ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3495]) ).

cnf(c_0_3496_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),top_top(fun(X1,bool))))
    | ti(X1,sk1_esk36_3(X1,X2,X3)) != ti(X1,sk1_esk35_3(X1,X2,X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3496]) ).

cnf(c_0_3496_1,axiom,
    ( ti(X1,sk1_esk36_3(X1,X2,X3)) != ti(X1,sk1_esk35_3(X1,X2,X3))
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X2),fun(fun(X1,bool),bool),inj_on(X1,X2),X3),top_top(fun(X1,bool)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3496]) ).

cnf(c_0_3497_0,axiom,
    ( X1 != zero_zero(nat)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_3497]) ).

cnf(c_0_3497_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
    | X1 != zero_zero(nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3497]) ).

cnf(c_0_3498_0,axiom,
    ( X1 = zero_zero(nat)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),zero_zero(nat))) ),
    inference(literals_permutation,[status(thm)],[c_0_3498]) ).

cnf(c_0_3498_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),zero_zero(nat)))
    | X1 = zero_zero(nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3498]) ).

cnf(c_0_3502_0,axiom,
    ( X1 != zero_zero(nat)
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_3502]) ).

cnf(c_0_3502_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1))
    | X1 != zero_zero(nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3502]) ).

cnf(c_0_3503_0,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | X1 != X2 ),
    inference(literals_permutation,[status(thm)],[c_0_3503]) ).

cnf(c_0_3503_1,axiom,
    ( X1 != X2
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3503]) ).

cnf(c_0_3504_0,axiom,
    ( X1 != X2
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3504]) ).

cnf(c_0_3504_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | X1 != X2 ),
    inference(literals_permutation,[status(thm)],[c_0_3504]) ).

cnf(c_0_3505_0,axiom,
    ( X1 != X2
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_3505]) ).

cnf(c_0_3505_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1))
    | X1 != X2 ),
    inference(literals_permutation,[status(thm)],[c_0_3505]) ).

cnf(c_0_3506_0,axiom,
    ( X1 != X2
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3506]) ).

cnf(c_0_3506_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X2))
    | X1 != X2 ),
    inference(literals_permutation,[status(thm)],[c_0_3506]) ).

cnf(c_0_3507_0,axiom,
    ( X1 != X2
    | ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_3507]) ).

cnf(c_0_3507_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X2),X1))
    | X1 != X2 ),
    inference(literals_permutation,[status(thm)],[c_0_3507]) ).

cnf(c_0_3510_0,axiom,
    ( X1 = X2
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X3) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3510]) ).

cnf(c_0_3510_1,axiom,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X3) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_3510]) ).

cnf(c_0_3511_0,axiom,
    ( X1 = X2
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X1) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3511]) ).

cnf(c_0_3511_1,axiom,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X1) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_3511]) ).

cnf(c_0_3512_0,axiom,
    ( hBOOL(X1)
    | hBOOL(X2)
    | ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X2),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_3512]) ).

cnf(c_0_3512_1,axiom,
    ( hBOOL(X2)
    | hBOOL(X1)
    | ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X2),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_3512]) ).

cnf(c_0_3512_2,axiom,
    ( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X2),X1))
    | hBOOL(X2)
    | hBOOL(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3512]) ).

cnf(c_0_3513_0,axiom,
    ( hBOOL(X1)
    | ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X2),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_3513]) ).

cnf(c_0_3513_1,axiom,
    ( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X2),X1))
    | hBOOL(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3513]) ).

cnf(c_0_3514_0,axiom,
    ( hBOOL(X1)
    | ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3514]) ).

cnf(c_0_3514_1,axiom,
    ( ~ hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X1),X2))
    | hBOOL(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3514]) ).

cnf(c_0_3515_0,axiom,
    ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X1))
    | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sk1_esk78_2(X2,X1)),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_3515]) ).

cnf(c_0_3515_1,axiom,
    ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sk1_esk78_2(X2,X1)),X1))
    | hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_3515]) ).

cnf(c_0_3516_0,axiom,
    ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X1))
    | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sk1_esk76_2(X1,X2)),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_3516]) ).

cnf(c_0_3516_1,axiom,
    ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sk1_esk76_2(X1,X2)),X1))
    | hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_3516]) ).

cnf(c_0_3517_0,axiom,
    ( hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X1))
    | hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sk1_esk74_2(X1,X2)),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_3517]) ).

cnf(c_0_3517_1,axiom,
    ( hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),sk1_esk74_2(X1,X2)),X1))
    | hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_3517]) ).

cnf(c_0_3518_0,axiom,
    ( ti(fun(X1,X2),X3) = ti(fun(X1,X2),X4)
    | hAPP(X1,X2,X3,sk1_esk20_4(X1,X2,X3,X4)) != hAPP(X1,X2,X4,sk1_esk20_4(X1,X2,X3,X4)) ),
    inference(literals_permutation,[status(thm)],[c_0_3518]) ).

cnf(c_0_3518_1,axiom,
    ( hAPP(X1,X2,X3,sk1_esk20_4(X1,X2,X3,X4)) != hAPP(X1,X2,X4,sk1_esk20_4(X1,X2,X3,X4))
    | ti(fun(X1,X2),X3) = ti(fun(X1,X2),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_3518]) ).

cnf(c_0_3519_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool))))
    | ~ hBOOL(hAPP(fun(fun(X2,X1),bool),bool,finite_finite_1(fun(X2,X1)),top_top(fun(fun(X2,X1),bool)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3519]) ).

cnf(c_0_3519_1,axiom,
    ( ~ hBOOL(hAPP(fun(fun(X2,X1),bool),bool,finite_finite_1(fun(X2,X1)),top_top(fun(fun(X2,X1),bool))))
    | hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3519]) ).

cnf(c_0_3520_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool))))
    | ~ hBOOL(hAPP(fun(sum_sum(X1,X2),bool),bool,finite_finite_1(sum_sum(X1,X2)),top_top(fun(sum_sum(X1,X2),bool)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3520]) ).

cnf(c_0_3520_1,axiom,
    ( ~ hBOOL(hAPP(fun(sum_sum(X1,X2),bool),bool,finite_finite_1(sum_sum(X1,X2)),top_top(fun(sum_sum(X1,X2),bool))))
    | hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3520]) ).

cnf(c_0_3521_0,axiom,
    ( hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),top_top(fun(X2,bool))))
    | ~ hBOOL(hAPP(fun(sum_sum(X1,X2),bool),bool,finite_finite_1(sum_sum(X1,X2)),top_top(fun(sum_sum(X1,X2),bool)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3521]) ).

cnf(c_0_3521_1,axiom,
    ( ~ hBOOL(hAPP(fun(sum_sum(X1,X2),bool),bool,finite_finite_1(sum_sum(X1,X2)),top_top(fun(sum_sum(X1,X2),bool))))
    | hBOOL(hAPP(fun(X2,bool),bool,finite_finite_1(X2),top_top(fun(X2,bool)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3521]) ).

cnf(c_0_3522_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3522]) ).

cnf(c_0_3522_1,axiom,
    ( ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3)
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3522]) ).

cnf(c_0_3523_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X2))
    | ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3523]) ).

cnf(c_0_3523_1,axiom,
    ( ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3)
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3523]) ).

cnf(c_0_3524_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3524]) ).

cnf(c_0_3524_1,axiom,
    ( ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3)
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3524]) ).

cnf(c_0_3525_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ti(fun(X1,bool),X3) != ti(fun(X1,bool),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3525]) ).

cnf(c_0_3525_1,axiom,
    ( ti(fun(X1,bool),X3) != ti(fun(X1,bool),X2)
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3525]) ).

cnf(c_0_3526_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3526]) ).

cnf(c_0_3526_1,axiom,
    ( ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3)
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3526]) ).

cnf(c_0_3527_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X2))
    | ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3527]) ).

cnf(c_0_3527_1,axiom,
    ( ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3)
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X3),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3527]) ).

cnf(c_0_3528_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3))
    | ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3528]) ).

cnf(c_0_3528_1,axiom,
    ( ti(fun(X1,bool),X2) != ti(fun(X1,bool),X3)
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3528]) ).

cnf(c_0_3532_0,axiom,
    ( X1 = hAPP(nat,nat,suc,zero_zero(nat))
    | X2 = hAPP(nat,nat,suc,zero_zero(nat))
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) != hAPP(nat,nat,suc,zero_zero(nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_3532]) ).

cnf(c_0_3532_1,axiom,
    ( X2 = hAPP(nat,nat,suc,zero_zero(nat))
    | X1 = hAPP(nat,nat,suc,zero_zero(nat))
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) != hAPP(nat,nat,suc,zero_zero(nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_3532]) ).

cnf(c_0_3532_2,axiom,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) != hAPP(nat,nat,suc,zero_zero(nat))
    | X2 = hAPP(nat,nat,suc,zero_zero(nat))
    | X1 = hAPP(nat,nat,suc,zero_zero(nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_3532]) ).

cnf(c_0_3533_0,axiom,
    ( X1 = hAPP(nat,nat,suc,zero_zero(nat))
    | X2 = hAPP(nat,nat,suc,zero_zero(nat))
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) != hAPP(nat,nat,suc,zero_zero(nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_3533]) ).

cnf(c_0_3533_1,axiom,
    ( X2 = hAPP(nat,nat,suc,zero_zero(nat))
    | X1 = hAPP(nat,nat,suc,zero_zero(nat))
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) != hAPP(nat,nat,suc,zero_zero(nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_3533]) ).

cnf(c_0_3533_2,axiom,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) != hAPP(nat,nat,suc,zero_zero(nat))
    | X2 = hAPP(nat,nat,suc,zero_zero(nat))
    | X1 = hAPP(nat,nat,suc,zero_zero(nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_3533]) ).

cnf(c_0_3535_0,axiom,
    ( hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
    | ~ hBOOL(hAPP(nat,bool,X1,X2))
    | ~ hBOOL(hAPP(nat,bool,X1,sk1_esk97_1(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_3535]) ).

cnf(c_0_3535_1,axiom,
    ( ~ hBOOL(hAPP(nat,bool,X1,X2))
    | hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
    | ~ hBOOL(hAPP(nat,bool,X1,sk1_esk97_1(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_3535]) ).

cnf(c_0_3535_2,axiom,
    ( ~ hBOOL(hAPP(nat,bool,X1,sk1_esk97_1(X1)))
    | ~ hBOOL(hAPP(nat,bool,X1,X2))
    | hBOOL(hAPP(nat,bool,X1,zero_zero(nat))) ),
    inference(literals_permutation,[status(thm)],[c_0_3535]) ).

cnf(c_0_3536_0,axiom,
    ( ti(fun(X1,bool),X2) = top_top(fun(X1,bool))
    | hAPP(fun(X1,bool),nat,finite_card(X1),X2) != hAPP(fun(X1,bool),nat,finite_card(X1),top_top(fun(X1,bool)))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3536]) ).

cnf(c_0_3536_1,axiom,
    ( hAPP(fun(X1,bool),nat,finite_card(X1),X2) != hAPP(fun(X1,bool),nat,finite_card(X1),top_top(fun(X1,bool)))
    | ti(fun(X1,bool),X2) = top_top(fun(X1,bool))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3536]) ).

cnf(c_0_3536_2,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool))))
    | hAPP(fun(X1,bool),nat,finite_card(X1),X2) != hAPP(fun(X1,bool),nat,finite_card(X1),top_top(fun(X1,bool)))
    | ti(fun(X1,bool),X2) = top_top(fun(X1,bool)) ),
    inference(literals_permutation,[status(thm)],[c_0_3536]) ).

cnf(c_0_3537_0,axiom,
    ( hAPP(X1,product_prod(X2,X1),hAPP(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),X3),X4) = hAPP(X1,product_prod(X2,X1),hAPP(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),X5),X6)
    | ti(X1,X4) != ti(X1,X6)
    | ti(X2,X3) != ti(X2,X5) ),
    inference(literals_permutation,[status(thm)],[c_0_3537]) ).

cnf(c_0_3537_1,axiom,
    ( ti(X1,X4) != ti(X1,X6)
    | hAPP(X1,product_prod(X2,X1),hAPP(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),X3),X4) = hAPP(X1,product_prod(X2,X1),hAPP(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),X5),X6)
    | ti(X2,X3) != ti(X2,X5) ),
    inference(literals_permutation,[status(thm)],[c_0_3537]) ).

cnf(c_0_3537_2,axiom,
    ( ti(X2,X3) != ti(X2,X5)
    | ti(X1,X4) != ti(X1,X6)
    | hAPP(X1,product_prod(X2,X1),hAPP(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),X3),X4) = hAPP(X1,product_prod(X2,X1),hAPP(X2,fun(X1,product_prod(X2,X1)),product_Pair(X2,X1),X5),X6) ),
    inference(literals_permutation,[status(thm)],[c_0_3537]) ).

cnf(c_0_3541_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
    | X1 != hAPP(nat,nat,suc,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3541]) ).

cnf(c_0_3541_1,axiom,
    ( X1 != hAPP(nat,nat,suc,X2)
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_3541]) ).

cnf(c_0_3546_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),one_one(X1)),ring_1_Ints(X1)))
    | ~ ring_1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3546]) ).

cnf(c_0_3546_1,axiom,
    ( ~ ring_1(X1)
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),one_one(X1)),ring_1_Ints(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_3546]) ).

cnf(c_0_3547_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),zero_zero(X1)),ring_1_Ints(X1)))
    | ~ ring_1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3547]) ).

cnf(c_0_3547_1,axiom,
    ( ~ ring_1(X1)
    | hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),zero_zero(X1)),ring_1_Ints(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_3547]) ).

cnf(c_0_3548_0,axiom,
    ( X1 = hAPP(nat,nat,suc,zero_zero(nat))
    | X1 = zero_zero(nat)
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) != hAPP(nat,nat,suc,zero_zero(nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_3548]) ).

cnf(c_0_3548_1,axiom,
    ( X1 = zero_zero(nat)
    | X1 = hAPP(nat,nat,suc,zero_zero(nat))
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) != hAPP(nat,nat,suc,zero_zero(nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_3548]) ).

cnf(c_0_3548_2,axiom,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) != hAPP(nat,nat,suc,zero_zero(nat))
    | X1 = zero_zero(nat)
    | X1 = hAPP(nat,nat,suc,zero_zero(nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_3548]) ).

cnf(c_0_3549_0,axiom,
    ( X2 = zero_zero(nat)
    | X2 = hAPP(nat,nat,suc,zero_zero(nat))
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) != hAPP(nat,nat,suc,zero_zero(nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_3549]) ).

cnf(c_0_3549_1,axiom,
    ( X2 = hAPP(nat,nat,suc,zero_zero(nat))
    | X2 = zero_zero(nat)
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) != hAPP(nat,nat,suc,zero_zero(nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_3549]) ).

cnf(c_0_3549_2,axiom,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) != hAPP(nat,nat,suc,zero_zero(nat))
    | X2 = hAPP(nat,nat,suc,zero_zero(nat))
    | X2 = zero_zero(nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3549]) ).

cnf(c_0_3550_0,axiom,
    ( X1 = hAPP(nat,nat,suc,zero_zero(nat))
    | X1 = zero_zero(nat)
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) != hAPP(nat,nat,suc,zero_zero(nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_3550]) ).

cnf(c_0_3550_1,axiom,
    ( X1 = zero_zero(nat)
    | X1 = hAPP(nat,nat,suc,zero_zero(nat))
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) != hAPP(nat,nat,suc,zero_zero(nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_3550]) ).

cnf(c_0_3550_2,axiom,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) != hAPP(nat,nat,suc,zero_zero(nat))
    | X1 = zero_zero(nat)
    | X1 = hAPP(nat,nat,suc,zero_zero(nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_3550]) ).

cnf(c_0_3551_0,axiom,
    ( X2 = zero_zero(nat)
    | X2 = hAPP(nat,nat,suc,zero_zero(nat))
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) != hAPP(nat,nat,suc,zero_zero(nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_3551]) ).

cnf(c_0_3551_1,axiom,
    ( X2 = hAPP(nat,nat,suc,zero_zero(nat))
    | X2 = zero_zero(nat)
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) != hAPP(nat,nat,suc,zero_zero(nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_3551]) ).

cnf(c_0_3551_2,axiom,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) != hAPP(nat,nat,suc,zero_zero(nat))
    | X2 = hAPP(nat,nat,suc,zero_zero(nat))
    | X2 = zero_zero(nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3551]) ).

cnf(c_0_3552_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool))))
    | ~ hBOOL(hAPP(fun(option(X1),bool),bool,finite_finite_1(option(X1)),top_top(fun(option(X1),bool)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3552]) ).

cnf(c_0_3552_1,axiom,
    ( ~ hBOOL(hAPP(fun(option(X1),bool),bool,finite_finite_1(option(X1)),top_top(fun(option(X1),bool))))
    | hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3552]) ).

cnf(c_0_3553_0,axiom,
    ( hBOOL(hAPP(nat,bool,X1,X2))
    | hBOOL(hAPP(nat,bool,X1,sk1_esk98_2(X2,X1)))
    | ~ hBOOL(hAPP(nat,bool,X1,zero_zero(nat))) ),
    inference(literals_permutation,[status(thm)],[c_0_3553]) ).

cnf(c_0_3553_1,axiom,
    ( hBOOL(hAPP(nat,bool,X1,sk1_esk98_2(X2,X1)))
    | hBOOL(hAPP(nat,bool,X1,X2))
    | ~ hBOOL(hAPP(nat,bool,X1,zero_zero(nat))) ),
    inference(literals_permutation,[status(thm)],[c_0_3553]) ).

cnf(c_0_3553_2,axiom,
    ( ~ hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
    | hBOOL(hAPP(nat,bool,X1,sk1_esk98_2(X2,X1)))
    | hBOOL(hAPP(nat,bool,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3553]) ).

cnf(c_0_3554_0,axiom,
    ( hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
    | hBOOL(hAPP(nat,bool,X1,sk1_esk81_2(X2,X1)))
    | ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3554]) ).

cnf(c_0_3554_1,axiom,
    ( hBOOL(hAPP(nat,bool,X1,sk1_esk81_2(X2,X1)))
    | hBOOL(hAPP(nat,bool,X1,zero_zero(nat)))
    | ~ hBOOL(hAPP(nat,bool,X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3554]) ).

cnf(c_0_3554_2,axiom,
    ( ~ hBOOL(hAPP(nat,bool,X1,X2))
    | hBOOL(hAPP(nat,bool,X1,sk1_esk81_2(X2,X1)))
    | hBOOL(hAPP(nat,bool,X1,zero_zero(nat))) ),
    inference(literals_permutation,[status(thm)],[c_0_3554]) ).

cnf(c_0_3555_0,axiom,
    ( hBOOL(hAPP(fun(option(X1),bool),bool,finite_finite_1(option(X1)),top_top(fun(option(X1),bool))))
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3555]) ).

cnf(c_0_3555_1,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool))))
    | hBOOL(hAPP(fun(option(X1),bool),bool,finite_finite_1(option(X1)),top_top(fun(option(X1),bool)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3555]) ).

cnf(c_0_3556_0,axiom,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)
    | ~ cancel_semigroup_add(X1)
    | ti(X1,X3) != ti(X1,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_3556]) ).

cnf(c_0_3556_1,axiom,
    ( ~ cancel_semigroup_add(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4)
    | ti(X1,X3) != ti(X1,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_3556]) ).

cnf(c_0_3556_2,axiom,
    ( ti(X1,X3) != ti(X1,X4)
    | ~ cancel_semigroup_add(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X4) ),
    inference(literals_permutation,[status(thm)],[c_0_3556]) ).

cnf(c_0_3557_0,axiom,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)
    | ~ cancel_semigroup_add(X1)
    | ti(X1,X2) != ti(X1,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_3557]) ).

cnf(c_0_3557_1,axiom,
    ( ~ cancel_semigroup_add(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3)
    | ti(X1,X2) != ti(X1,X4) ),
    inference(literals_permutation,[status(thm)],[c_0_3557]) ).

cnf(c_0_3557_2,axiom,
    ( ti(X1,X2) != ti(X1,X4)
    | ~ cancel_semigroup_add(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X4),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3557]) ).

cnf(c_0_3558_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),top_top(X1)),X2))
    | ~ top(X1)
    | ti(X1,X2) != top_top(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3558]) ).

cnf(c_0_3558_1,axiom,
    ( ~ top(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),top_top(X1)),X2))
    | ti(X1,X2) != top_top(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3558]) ).

cnf(c_0_3558_2,axiom,
    ( ti(X1,X2) != top_top(X1)
    | ~ top(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),top_top(X1)),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3558]) ).

cnf(c_0_3559_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ order(X1)
    | ti(X1,X2) != ti(X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3559]) ).

cnf(c_0_3559_1,axiom,
    ( ~ order(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ti(X1,X2) != ti(X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3559]) ).

cnf(c_0_3559_2,axiom,
    ( ti(X1,X2) != ti(X1,X3)
    | ~ order(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3559]) ).

cnf(c_0_3560_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ order(X1)
    | ti(X1,X2) != ti(X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3560]) ).

cnf(c_0_3560_1,axiom,
    ( ~ order(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ti(X1,X2) != ti(X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3560]) ).

cnf(c_0_3560_2,axiom,
    ( ti(X1,X2) != ti(X1,X3)
    | ~ order(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3560]) ).

cnf(c_0_3561_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ~ order(X1)
    | ti(X1,X2) != ti(X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3561]) ).

cnf(c_0_3561_1,axiom,
    ( ~ order(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2))
    | ti(X1,X2) != ti(X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3561]) ).

cnf(c_0_3561_2,axiom,
    ( ti(X1,X2) != ti(X1,X3)
    | ~ order(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X3),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3561]) ).

cnf(c_0_3562_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),fequal(X1),X2),X3))
    | ti(X1,X2) != ti(X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3562]) ).

cnf(c_0_3562_1,axiom,
    ( ti(X1,X2) != ti(X1,X3)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),fequal(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3562]) ).

cnf(c_0_3563_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),one_one(X1)))
    | ~ linordered_semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3563]) ).

cnf(c_0_3563_1,axiom,
    ( ~ linordered_semidom(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),zero_zero(X1)),one_one(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_3563]) ).

cnf(c_0_3564_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),one_one(X1)))
    | ~ linordered_semidom(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3564]) ).

cnf(c_0_3564_1,axiom,
    ( ~ linordered_semidom(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),zero_zero(X1)),one_one(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_3564]) ).

cnf(c_0_3565_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),top_top(X1)))
    | ti(X1,X2) = top_top(X1)
    | ~ top(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3565]) ).

cnf(c_0_3565_1,axiom,
    ( ti(X1,X2) = top_top(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),top_top(X1)))
    | ~ top(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3565]) ).

cnf(c_0_3565_2,axiom,
    ( ~ top(X1)
    | ti(X1,X2) = top_top(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),top_top(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_3565]) ).

cnf(c_0_3566_0,axiom,
    ( X2 = zero_zero(nat)
    | X1 = zero_zero(nat)
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) != hAPP(nat,nat,suc,zero_zero(nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_3566]) ).

cnf(c_0_3566_1,axiom,
    ( X1 = zero_zero(nat)
    | X2 = zero_zero(nat)
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) != hAPP(nat,nat,suc,zero_zero(nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_3566]) ).

cnf(c_0_3566_2,axiom,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) != hAPP(nat,nat,suc,zero_zero(nat))
    | X1 = zero_zero(nat)
    | X2 = zero_zero(nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3566]) ).

cnf(c_0_3567_0,axiom,
    ( X2 = zero_zero(nat)
    | X1 = zero_zero(nat)
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) != hAPP(nat,nat,suc,zero_zero(nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_3567]) ).

cnf(c_0_3567_1,axiom,
    ( X1 = zero_zero(nat)
    | X2 = zero_zero(nat)
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) != hAPP(nat,nat,suc,zero_zero(nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_3567]) ).

cnf(c_0_3567_2,axiom,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) != hAPP(nat,nat,suc,zero_zero(nat))
    | X1 = zero_zero(nat)
    | X2 = zero_zero(nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3567]) ).

cnf(c_0_3568_0,axiom,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X2)
    | ~ comm_semiring_1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3568]) ).

cnf(c_0_3568_1,axiom,
    ( ~ comm_semiring_1(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) = hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3568]) ).

cnf(c_0_3569_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),top_top(X1)))
    | ~ top(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3569]) ).

cnf(c_0_3569_1,axiom,
    ( ~ top(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),top_top(X1))) ),
    inference(literals_permutation,[status(thm)],[c_0_3569]) ).

cnf(c_0_3571_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | X2 != X3
    | ~ preorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3571]) ).

cnf(c_0_3571_1,axiom,
    ( X2 != X3
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3))
    | ~ preorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3571]) ).

cnf(c_0_3571_2,axiom,
    ( ~ preorder(X1)
    | X2 != X3
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X3)) ),
    inference(literals_permutation,[status(thm)],[c_0_3571]) ).

cnf(c_0_3572_0,axiom,
    ( hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X2))
    | ~ preorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3572]) ).

cnf(c_0_3572_1,axiom,
    ( ~ preorder(X1)
    | hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less_eq(X1),X2),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3572]) ).

cnf(c_0_3573_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
    | X1 = zero_zero(nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3573]) ).

cnf(c_0_3573_1,axiom,
    ( X1 = zero_zero(nat)
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_3573]) ).

cnf(c_0_3574_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1))
    | X1 = zero_zero(nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3574]) ).

cnf(c_0_3574_1,axiom,
    ( X1 = zero_zero(nat)
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_3574]) ).

cnf(c_0_3577_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),zero_zero(nat)))
    | X1 != zero_zero(nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3577]) ).

cnf(c_0_3577_1,axiom,
    ( X1 != zero_zero(nat)
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),zero_zero(nat))) ),
    inference(literals_permutation,[status(thm)],[c_0_3577]) ).

cnf(c_0_3578_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | X1 != X2 ),
    inference(literals_permutation,[status(thm)],[c_0_3578]) ).

cnf(c_0_3578_1,axiom,
    ( X1 != X2
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3578]) ).

cnf(c_0_3579_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | X1 != X2 ),
    inference(literals_permutation,[status(thm)],[c_0_3579]) ).

cnf(c_0_3579_1,axiom,
    ( X1 != X2
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3579]) ).

cnf(c_0_3580_0,axiom,
    ( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2))
    | X1 != X2 ),
    inference(literals_permutation,[status(thm)],[c_0_3580]) ).

cnf(c_0_3580_1,axiom,
    ( X1 != X2
    | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3580]) ).

cnf(c_0_3581_0,axiom,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X2)
    | X1 != X3 ),
    inference(literals_permutation,[status(thm)],[c_0_3581]) ).

cnf(c_0_3581_1,axiom,
    ( X1 != X3
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X3),X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3581]) ).

cnf(c_0_3582_0,axiom,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X3)
    | X2 != X3 ),
    inference(literals_permutation,[status(thm)],[c_0_3582]) ).

cnf(c_0_3582_1,axiom,
    ( X2 != X3
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3582]) ).

cnf(c_0_3585_0,axiom,
    ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X1),X2))
    | ~ hBOOL(X2)
    | ~ hBOOL(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3585]) ).

cnf(c_0_3585_1,axiom,
    ( ~ hBOOL(X2)
    | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X1),X2))
    | ~ hBOOL(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3585]) ).

cnf(c_0_3585_2,axiom,
    ( ~ hBOOL(X1)
    | ~ hBOOL(X2)
    | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3585]) ).

cnf(c_0_3586_0,axiom,
    ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X1),X2))
    | ~ hBOOL(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3586]) ).

cnf(c_0_3586_1,axiom,
    ( ~ hBOOL(X2)
    | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3586]) ).

cnf(c_0_3587_0,axiom,
    ( hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X1),X2))
    | ~ hBOOL(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3587]) ).

cnf(c_0_3587_1,axiom,
    ( ~ hBOOL(X1)
    | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3587]) ).

cnf(c_0_3588_0,axiom,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) = hAPP(nat,nat,suc,zero_zero(nat))
    | X2 != zero_zero(nat)
    | X1 != hAPP(nat,nat,suc,zero_zero(nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_3588]) ).

cnf(c_0_3588_1,axiom,
    ( X2 != zero_zero(nat)
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) = hAPP(nat,nat,suc,zero_zero(nat))
    | X1 != hAPP(nat,nat,suc,zero_zero(nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_3588]) ).

cnf(c_0_3588_2,axiom,
    ( X1 != hAPP(nat,nat,suc,zero_zero(nat))
    | X2 != zero_zero(nat)
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) = hAPP(nat,nat,suc,zero_zero(nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_3588]) ).

cnf(c_0_3589_0,axiom,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) = hAPP(nat,nat,suc,zero_zero(nat))
    | X2 != hAPP(nat,nat,suc,zero_zero(nat))
    | X1 != zero_zero(nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3589]) ).

cnf(c_0_3589_1,axiom,
    ( X2 != hAPP(nat,nat,suc,zero_zero(nat))
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) = hAPP(nat,nat,suc,zero_zero(nat))
    | X1 != zero_zero(nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3589]) ).

cnf(c_0_3589_2,axiom,
    ( X1 != zero_zero(nat)
    | X2 != hAPP(nat,nat,suc,zero_zero(nat))
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) = hAPP(nat,nat,suc,zero_zero(nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_3589]) ).

cnf(c_0_3590_0,axiom,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) = hAPP(nat,nat,suc,zero_zero(nat))
    | X2 != zero_zero(nat)
    | X1 != hAPP(nat,nat,suc,zero_zero(nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_3590]) ).

cnf(c_0_3590_1,axiom,
    ( X2 != zero_zero(nat)
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) = hAPP(nat,nat,suc,zero_zero(nat))
    | X1 != hAPP(nat,nat,suc,zero_zero(nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_3590]) ).

cnf(c_0_3590_2,axiom,
    ( X1 != hAPP(nat,nat,suc,zero_zero(nat))
    | X2 != zero_zero(nat)
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) = hAPP(nat,nat,suc,zero_zero(nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_3590]) ).

cnf(c_0_3591_0,axiom,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) = hAPP(nat,nat,suc,zero_zero(nat))
    | X2 != hAPP(nat,nat,suc,zero_zero(nat))
    | X1 != zero_zero(nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3591]) ).

cnf(c_0_3591_1,axiom,
    ( X2 != hAPP(nat,nat,suc,zero_zero(nat))
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) = hAPP(nat,nat,suc,zero_zero(nat))
    | X1 != zero_zero(nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3591]) ).

cnf(c_0_3591_2,axiom,
    ( X1 != zero_zero(nat)
    | X2 != hAPP(nat,nat,suc,zero_zero(nat))
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) = hAPP(nat,nat,suc,zero_zero(nat)) ),
    inference(literals_permutation,[status(thm)],[c_0_3591]) ).

cnf(c_0_3594_0,axiom,
    ( ti(X1,X2) = zero_zero(X1)
    | ~ semiri456707255roduct(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X2) != ti(X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3594]) ).

cnf(c_0_3594_1,axiom,
    ( ~ semiri456707255roduct(X1)
    | ti(X1,X2) = zero_zero(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X2) != ti(X1,X3) ),
    inference(literals_permutation,[status(thm)],[c_0_3594]) ).

cnf(c_0_3594_2,axiom,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X3),X2) != ti(X1,X3)
    | ~ semiri456707255roduct(X1)
    | ti(X1,X2) = zero_zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3594]) ).

cnf(c_0_3595_0,axiom,
    ( ti(X1,X2) = zero_zero(X1)
    | ~ linord219039673up_add(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2) != zero_zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3595]) ).

cnf(c_0_3595_1,axiom,
    ( ~ linord219039673up_add(X1)
    | ti(X1,X2) = zero_zero(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2) != zero_zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3595]) ).

cnf(c_0_3595_2,axiom,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2) != zero_zero(X1)
    | ~ linord219039673up_add(X1)
    | ti(X1,X2) = zero_zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3595]) ).

cnf(c_0_3596_0,axiom,
    ( ti(X1,X2) = zero_zero(X1)
    | ~ linord219039673up_add(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2) != zero_zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3596]) ).

cnf(c_0_3596_1,axiom,
    ( ~ linord219039673up_add(X1)
    | ti(X1,X2) = zero_zero(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2) != zero_zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3596]) ).

cnf(c_0_3596_2,axiom,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2) != zero_zero(X1)
    | ~ linord219039673up_add(X1)
    | ti(X1,X2) = zero_zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3596]) ).

cnf(c_0_3597_0,axiom,
    ( X1 = zero_zero(nat)
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) != zero_zero(nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3597]) ).

cnf(c_0_3597_1,axiom,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) != zero_zero(nat)
    | X1 = zero_zero(nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3597]) ).

cnf(c_0_3598_0,axiom,
    ( X2 = zero_zero(nat)
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) != zero_zero(nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3598]) ).

cnf(c_0_3598_1,axiom,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) != zero_zero(nat)
    | X2 = zero_zero(nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3598]) ).

cnf(c_0_3599_0,axiom,
    ( X1 = zero_zero(nat)
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X1) != X2 ),
    inference(literals_permutation,[status(thm)],[c_0_3599]) ).

cnf(c_0_3599_1,axiom,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X1) != X2
    | X1 = zero_zero(nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3599]) ).

cnf(c_0_3601_0,axiom,
    ( hAPP(fun(X1,bool),nat,finite_card(X1),X2) = zero_zero(nat)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | zero_zero(nat) != one_one(nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3601]) ).

cnf(c_0_3601_1,axiom,
    ( ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | hAPP(fun(X1,bool),nat,finite_card(X1),X2) = zero_zero(nat)
    | zero_zero(nat) != one_one(nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3601]) ).

cnf(c_0_3601_2,axiom,
    ( zero_zero(nat) != one_one(nat)
    | ~ hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | hAPP(fun(X1,bool),nat,finite_card(X1),X2) = zero_zero(nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3601]) ).

cnf(c_0_3612_0,axiom,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) = ti(X1,X2)
    | ~ semiri456707255roduct(X1)
    | ti(X1,X3) != zero_zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3612]) ).

cnf(c_0_3612_1,axiom,
    ( ~ semiri456707255roduct(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) = ti(X1,X2)
    | ti(X1,X3) != zero_zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3612]) ).

cnf(c_0_3612_2,axiom,
    ( ti(X1,X3) != zero_zero(X1)
    | ~ semiri456707255roduct(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X3) = ti(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3612]) ).

cnf(c_0_3613_0,axiom,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2) = zero_zero(X1)
    | ~ linord219039673up_add(X1)
    | ti(X1,X2) != zero_zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3613]) ).

cnf(c_0_3613_1,axiom,
    ( ~ linord219039673up_add(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2) = zero_zero(X1)
    | ti(X1,X2) != zero_zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3613]) ).

cnf(c_0_3613_2,axiom,
    ( ti(X1,X2) != zero_zero(X1)
    | ~ linord219039673up_add(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2) = zero_zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3613]) ).

cnf(c_0_3614_0,axiom,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2) = zero_zero(X1)
    | ~ linord219039673up_add(X1)
    | ti(X1,X2) != zero_zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3614]) ).

cnf(c_0_3614_1,axiom,
    ( ~ linord219039673up_add(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2) = zero_zero(X1)
    | ti(X1,X2) != zero_zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3614]) ).

cnf(c_0_3614_2,axiom,
    ( ti(X1,X2) != zero_zero(X1)
    | ~ linord219039673up_add(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),X2) = zero_zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3614]) ).

cnf(c_0_3615_0,axiom,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),zero_zero(X1)),X2) = ti(X1,X2)
    | ~ comm_semiring_1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3615]) ).

cnf(c_0_3615_1,axiom,
    ( ~ comm_semiring_1(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),zero_zero(X1)),X2) = ti(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3615]) ).

cnf(c_0_3616_0,axiom,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),zero_zero(X1)),X2) = ti(X1,X2)
    | ~ monoid_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3616]) ).

cnf(c_0_3616_1,axiom,
    ( ~ monoid_add(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),zero_zero(X1)),X2) = ti(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3616]) ).

cnf(c_0_3617_0,axiom,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),zero_zero(X1)),X2) = ti(X1,X2)
    | ~ comm_monoid_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3617]) ).

cnf(c_0_3617_1,axiom,
    ( ~ comm_monoid_add(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),zero_zero(X1)),X2) = ti(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3617]) ).

cnf(c_0_3618_0,axiom,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),zero_zero(X1)) = ti(X1,X2)
    | ~ comm_semiring_1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3618]) ).

cnf(c_0_3618_1,axiom,
    ( ~ comm_semiring_1(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),zero_zero(X1)) = ti(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3618]) ).

cnf(c_0_3619_0,axiom,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),zero_zero(X1)) = ti(X1,X2)
    | ~ monoid_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3619]) ).

cnf(c_0_3619_1,axiom,
    ( ~ monoid_add(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),zero_zero(X1)) = ti(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3619]) ).

cnf(c_0_3620_0,axiom,
    ( hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),zero_zero(X1)) = ti(X1,X2)
    | ~ comm_monoid_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3620]) ).

cnf(c_0_3620_1,axiom,
    ( ~ comm_monoid_add(X1)
    | hAPP(X1,X1,hAPP(X1,fun(X1,X1),plus_plus(X1),X2),zero_zero(X1)) = ti(X1,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3620]) ).

cnf(c_0_3621_0,axiom,
    ( hAPP(fun(X1,bool),nat,finite_card(X1),X2) = zero_zero(nat)
    | hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3621]) ).

cnf(c_0_3621_1,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | hAPP(fun(X1,bool),nat,finite_card(X1),X2) = zero_zero(nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3621]) ).

cnf(c_0_3622_0,axiom,
    ( hAPP(fun(X1,bool),nat,finite_card(X1),X2) = zero_zero(nat)
    | hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3622]) ).

cnf(c_0_3622_1,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | hAPP(fun(X1,bool),nat,finite_card(X1),X2) = zero_zero(nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3622]) ).

cnf(c_0_3625_0,axiom,
    ( hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) = zero_zero(nat)
    | X2 != zero_zero(nat)
    | X1 != zero_zero(nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3625]) ).

cnf(c_0_3625_1,axiom,
    ( X2 != zero_zero(nat)
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) = zero_zero(nat)
    | X1 != zero_zero(nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3625]) ).

cnf(c_0_3625_2,axiom,
    ( X1 != zero_zero(nat)
    | X2 != zero_zero(nat)
    | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) = zero_zero(nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3625]) ).

cnf(c_0_3628_0,axiom,
    ( ~ hBOOL(X1)
    | ~ hBOOL(hAPP(bool,bool,fNot,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_3628]) ).

cnf(c_0_3628_1,axiom,
    ( ~ hBOOL(hAPP(bool,bool,fNot,X1))
    | ~ hBOOL(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3628]) ).

cnf(c_0_3629_0,axiom,
    ( X1 = X2
    | hAPP(nat,nat,suc,X1) != hAPP(nat,nat,suc,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3629]) ).

cnf(c_0_3629_1,axiom,
    ( hAPP(nat,nat,suc,X1) != hAPP(nat,nat,suc,X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_3629]) ).

cnf(c_0_3630_0,axiom,
    ( X1 = X2
    | hAPP(nat,nat,suc,X1) != hAPP(nat,nat,suc,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3630]) ).

cnf(c_0_3630_1,axiom,
    ( hAPP(nat,nat,suc,X1) != hAPP(nat,nat,suc,X2)
    | X1 = X2 ),
    inference(literals_permutation,[status(thm)],[c_0_3630]) ).

cnf(c_0_3633_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool))))
    | ~ finite_finite(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3633]) ).

cnf(c_0_3633_1,axiom,
    ( ~ finite_finite(X1)
    | hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),top_top(fun(X1,bool)))) ),
    inference(literals_permutation,[status(thm)],[c_0_3633]) ).

cnf(c_0_3639_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ finite_finite(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3639]) ).

cnf(c_0_3639_1,axiom,
    ( ~ finite_finite(X1)
    | hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3639]) ).

cnf(c_0_3640_0,axiom,
    ( hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2))
    | ~ finite_finite(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3640]) ).

cnf(c_0_3640_1,axiom,
    ( ~ finite_finite(X1)
    | hBOOL(hAPP(fun(X1,bool),bool,finite_finite_1(X1),X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3640]) ).

cnf(c_0_3645_0,axiom,
    ( hBOOL(hAPP(bool,bool,fNot,X1))
    | hBOOL(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3645]) ).

cnf(c_0_3645_1,axiom,
    ( hBOOL(X1)
    | hBOOL(hAPP(bool,bool,fNot,X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_3645]) ).

cnf(c_0_3646_0,axiom,
    ( hAPP(nat,nat,suc,X1) = hAPP(nat,nat,suc,X2)
    | X1 != X2 ),
    inference(literals_permutation,[status(thm)],[c_0_3646]) ).

cnf(c_0_3646_1,axiom,
    ( X1 != X2
    | hAPP(nat,nat,suc,X1) = hAPP(nat,nat,suc,X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3646]) ).

cnf(c_0_3663_0,axiom,
    ( hAPP(X1,X2,top_top(fun(X1,X2)),X3) = top_top(X2)
    | ~ top(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3663]) ).

cnf(c_0_3663_1,axiom,
    ( ~ top(X2)
    | hAPP(X1,X2,top_top(fun(X1,X2)),X3) = top_top(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3663]) ).

cnf(c_0_3666_0,axiom,
    ( hAPP(nat,nat,suc,sk1_esk96_1(X1)) = X1
    | X1 = zero_zero(nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3666]) ).

cnf(c_0_3666_1,axiom,
    ( X1 = zero_zero(nat)
    | hAPP(nat,nat,suc,sk1_esk96_1(X1)) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_3666]) ).

cnf(c_0_3667_0,axiom,
    ( hAPP(nat,nat,suc,sk1_esk95_1(X1)) = X1
    | X1 = zero_zero(nat) ),
    inference(literals_permutation,[status(thm)],[c_0_3667]) ).

cnf(c_0_3667_1,axiom,
    ( X1 = zero_zero(nat)
    | hAPP(nat,nat,suc,sk1_esk95_1(X1)) = X1 ),
    inference(literals_permutation,[status(thm)],[c_0_3667]) ).

cnf(c_0_3671_0,axiom,
    ( ti(fun(X1,fun(X1,fun(X1,bool))),ord_atLeastLessThan(X1)) = ord_atLeastLessThan(X1)
    | ~ linorder(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3671]) ).

cnf(c_0_3671_1,axiom,
    ( ~ linorder(X1)
    | ti(fun(X1,fun(X1,fun(X1,bool))),ord_atLeastLessThan(X1)) = ord_atLeastLessThan(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3671]) ).

cnf(c_0_3676_0,axiom,
    ( ti(fun(X1,fun(X1,X1)),plus_plus(X1)) = plus_plus(X1)
    | ~ cancel_semigroup_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3676]) ).

cnf(c_0_3676_1,axiom,
    ( ~ cancel_semigroup_add(X1)
    | ti(fun(X1,fun(X1,X1)),plus_plus(X1)) = plus_plus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3676]) ).

cnf(c_0_3677_0,axiom,
    ( ti(fun(X1,fun(X1,X1)),plus_plus(X1)) = plus_plus(X1)
    | ~ ab_semigroup_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3677]) ).

cnf(c_0_3677_1,axiom,
    ( ~ ab_semigroup_add(X1)
    | ti(fun(X1,fun(X1,X1)),plus_plus(X1)) = plus_plus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3677]) ).

cnf(c_0_3678_0,axiom,
    ( ti(fun(X1,fun(X1,X1)),plus_plus(X1)) = plus_plus(X1)
    | ~ monoid_add(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3678]) ).

cnf(c_0_3678_1,axiom,
    ( ~ monoid_add(X1)
    | ti(fun(X1,fun(X1,X1)),plus_plus(X1)) = plus_plus(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3678]) ).

cnf(c_0_3679_0,axiom,
    ( ti(fun(X1,fun(X1,bool)),ord_less_eq(X1)) = ord_less_eq(X1)
    | ~ ord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3679]) ).

cnf(c_0_3679_1,axiom,
    ( ~ ord(X1)
    | ti(fun(X1,fun(X1,bool)),ord_less_eq(X1)) = ord_less_eq(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3679]) ).

cnf(c_0_3680_0,axiom,
    ( ti(fun(X1,fun(X1,bool)),ord_less(X1)) = ord_less(X1)
    | ~ ord(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3680]) ).

cnf(c_0_3680_1,axiom,
    ( ~ ord(X1)
    | ti(fun(X1,fun(X1,bool)),ord_less(X1)) = ord_less(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3680]) ).

cnf(c_0_3688_0,axiom,
    ( ti(fun(X1,bool),ring_1_Ints(X1)) = ring_1_Ints(X1)
    | ~ ring_1(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3688]) ).

cnf(c_0_3688_1,axiom,
    ( ~ ring_1(X1)
    | ti(fun(X1,bool),ring_1_Ints(X1)) = ring_1_Ints(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3688]) ).

cnf(c_0_3689_0,axiom,
    ( ti(X1,X2) = zero_zero(X1)
    | ~ zero(X1)
    | ti(X1,X2) != zero_zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3689]) ).

cnf(c_0_3689_1,axiom,
    ( ~ zero(X1)
    | ti(X1,X2) = zero_zero(X1)
    | ti(X1,X2) != zero_zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3689]) ).

cnf(c_0_3689_2,axiom,
    ( ti(X1,X2) != zero_zero(X1)
    | ~ zero(X1)
    | ti(X1,X2) = zero_zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3689]) ).

cnf(c_0_3690_0,axiom,
    ( ti(X1,X2) = zero_zero(X1)
    | ~ zero(X1)
    | ti(X1,X2) != zero_zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3690]) ).

cnf(c_0_3690_1,axiom,
    ( ~ zero(X1)
    | ti(X1,X2) = zero_zero(X1)
    | ti(X1,X2) != zero_zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3690]) ).

cnf(c_0_3690_2,axiom,
    ( ti(X1,X2) != zero_zero(X1)
    | ~ zero(X1)
    | ti(X1,X2) = zero_zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3690]) ).

cnf(c_0_3691_0,axiom,
    ( ti(X1,X2) = one_one(X1)
    | ~ one(X1)
    | ti(X1,X2) != one_one(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3691]) ).

cnf(c_0_3691_1,axiom,
    ( ~ one(X1)
    | ti(X1,X2) = one_one(X1)
    | ti(X1,X2) != one_one(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3691]) ).

cnf(c_0_3691_2,axiom,
    ( ti(X1,X2) != one_one(X1)
    | ~ one(X1)
    | ti(X1,X2) = one_one(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3691]) ).

cnf(c_0_3692_0,axiom,
    ( ti(X1,X2) = one_one(X1)
    | ~ one(X1)
    | ti(X1,X2) != one_one(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3692]) ).

cnf(c_0_3692_1,axiom,
    ( ~ one(X1)
    | ti(X1,X2) = one_one(X1)
    | ti(X1,X2) != one_one(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3692]) ).

cnf(c_0_3692_2,axiom,
    ( ti(X1,X2) != one_one(X1)
    | ~ one(X1)
    | ti(X1,X2) = one_one(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3692]) ).

cnf(c_0_3695_0,axiom,
    ( finite_finite(product_prod(X1,X2))
    | ~ finite_finite(X1)
    | ~ finite_finite(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3695]) ).

cnf(c_0_3695_1,axiom,
    ( ~ finite_finite(X1)
    | finite_finite(product_prod(X1,X2))
    | ~ finite_finite(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3695]) ).

cnf(c_0_3695_2,axiom,
    ( ~ finite_finite(X2)
    | ~ finite_finite(X1)
    | finite_finite(product_prod(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3695]) ).

cnf(c_0_3696_0,axiom,
    ( finite_finite(sum_sum(X1,X2))
    | ~ finite_finite(X1)
    | ~ finite_finite(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3696]) ).

cnf(c_0_3696_1,axiom,
    ( ~ finite_finite(X1)
    | finite_finite(sum_sum(X1,X2))
    | ~ finite_finite(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3696]) ).

cnf(c_0_3696_2,axiom,
    ( ~ finite_finite(X2)
    | ~ finite_finite(X1)
    | finite_finite(sum_sum(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3696]) ).

cnf(c_0_3697_0,axiom,
    ( finite_finite(fun(X1,X2))
    | ~ finite_finite(X1)
    | ~ finite_finite(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3697]) ).

cnf(c_0_3697_1,axiom,
    ( ~ finite_finite(X1)
    | finite_finite(fun(X1,X2))
    | ~ finite_finite(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3697]) ).

cnf(c_0_3697_2,axiom,
    ( ~ finite_finite(X2)
    | ~ finite_finite(X1)
    | finite_finite(fun(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3697]) ).

cnf(c_0_3698_0,axiom,
    ( ord(fun(X1,X2))
    | ~ ord(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3698]) ).

cnf(c_0_3698_1,axiom,
    ( ~ ord(X2)
    | ord(fun(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3698]) ).

cnf(c_0_3699_0,axiom,
    ( top(fun(X1,X2))
    | ~ top(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3699]) ).

cnf(c_0_3699_1,axiom,
    ( ~ top(X2)
    | top(fun(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3699]) ).

cnf(c_0_3700_0,axiom,
    ( order(fun(X1,X2))
    | ~ order(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3700]) ).

cnf(c_0_3700_1,axiom,
    ( ~ order(X2)
    | order(fun(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3700]) ).

cnf(c_0_3701_0,axiom,
    ( preorder(fun(X1,X2))
    | ~ preorder(X2) ),
    inference(literals_permutation,[status(thm)],[c_0_3701]) ).

cnf(c_0_3701_1,axiom,
    ( ~ preorder(X2)
    | preorder(fun(X1,X2)) ),
    inference(literals_permutation,[status(thm)],[c_0_3701]) ).

cnf(c_0_3705_0,axiom,
    ( ti(X1,top_top(X1)) = top_top(X1)
    | ~ top(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3705]) ).

cnf(c_0_3705_1,axiom,
    ( ~ top(X1)
    | ti(X1,top_top(X1)) = top_top(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3705]) ).

cnf(c_0_3706_0,axiom,
    ( ti(X1,zero_zero(X1)) = zero_zero(X1)
    | ~ zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3706]) ).

cnf(c_0_3706_1,axiom,
    ( ~ zero(X1)
    | ti(X1,zero_zero(X1)) = zero_zero(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3706]) ).

cnf(c_0_3707_0,axiom,
    ( ti(X1,one_one(X1)) = one_one(X1)
    | ~ one(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3707]) ).

cnf(c_0_3707_1,axiom,
    ( ~ one(X1)
    | ti(X1,one_one(X1)) = one_one(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3707]) ).

cnf(c_0_3708_0,axiom,
    ( ti(bool,X1) = fFalse
    | ti(bool,X1) = fTrue ),
    inference(literals_permutation,[status(thm)],[c_0_3708]) ).

cnf(c_0_3708_1,axiom,
    ( ti(bool,X1) = fTrue
    | ti(bool,X1) = fFalse ),
    inference(literals_permutation,[status(thm)],[c_0_3708]) ).

cnf(c_0_3709_0,axiom,
    ( ti(bool,X1) = fFalse
    | ti(bool,X1) = fTrue ),
    inference(literals_permutation,[status(thm)],[c_0_3709]) ).

cnf(c_0_3709_1,axiom,
    ( ti(bool,X1) = fTrue
    | ti(bool,X1) = fFalse ),
    inference(literals_permutation,[status(thm)],[c_0_3709]) ).

cnf(c_0_3711_0,axiom,
    ( zero_zero(X1) != one_one(X1)
    | ~ zero_neq_one(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3711]) ).

cnf(c_0_3711_1,axiom,
    ( ~ zero_neq_one(X1)
    | zero_zero(X1) != one_one(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3711]) ).

cnf(c_0_3712_0,axiom,
    ( zero_zero(X1) != one_one(X1)
    | ~ zero_neq_one(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3712]) ).

cnf(c_0_3712_1,axiom,
    ( ~ zero_neq_one(X1)
    | zero_zero(X1) != one_one(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3712]) ).

cnf(c_0_3713_0,axiom,
    ( finite_finite(option(X1))
    | ~ finite_finite(X1) ),
    inference(literals_permutation,[status(thm)],[c_0_3713]) ).

cnf(c_0_3713_1,axiom,
    ( ~ finite_finite(X1)
    | finite_finite(option(X1)) ),
    inference(literals_permutation,[status(thm)],[c_0_3713]) ).

cnf(c_0_3074_0,axiom,
    ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lab)),
    inference(literals_permutation,[status(thm)],[c_0_3074]) ).

cnf(c_0_3075_0,axiom,
    ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lba)),
    inference(literals_permutation,[status(thm)],[c_0_3075]) ).

cnf(c_0_3116_0,axiom,
    ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),X2)),
    inference(literals_permutation,[status(thm)],[c_0_3116]) ).

cnf(c_0_3117_0,axiom,
    ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),X1)),
    inference(literals_permutation,[status(thm)],[c_0_3117]) ).

cnf(c_0_3298_0,axiom,
    ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)),X1)),
    inference(literals_permutation,[status(thm)],[c_0_3298]) ).

cnf(c_0_3499_0,axiom,
    ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),zero_zero(nat))),
    inference(literals_permutation,[status(thm)],[c_0_3499]) ).

cnf(c_0_3500_0,axiom,
    ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),zero_zero(nat))),
    inference(literals_permutation,[status(thm)],[c_0_3500]) ).

cnf(c_0_3501_0,axiom,
    ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),zero_zero(nat))),
    inference(literals_permutation,[status(thm)],[c_0_3501]) ).

cnf(c_0_3508_0,axiom,
    ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X1)),
    inference(literals_permutation,[status(thm)],[c_0_3508]) ).

cnf(c_0_3509_0,axiom,
    ~ hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),X1)),
    inference(literals_permutation,[status(thm)],[c_0_3509]) ).

cnf(c_0_3605_0,axiom,
    ~ hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),top_top(fun(nat,bool)))),
    inference(literals_permutation,[status(thm)],[c_0_3605]) ).

cnf(c_0_3649_0,axiom,
    hAPP(nat,nat,suc,X1) != zero_zero(nat),
    inference(literals_permutation,[status(thm)],[c_0_3649]) ).

cnf(c_0_3650_0,axiom,
    hAPP(nat,nat,suc,X1) != zero_zero(nat),
    inference(literals_permutation,[status(thm)],[c_0_3650]) ).

cnf(c_0_3651_0,axiom,
    hAPP(nat,nat,suc,X1) != zero_zero(nat),
    inference(literals_permutation,[status(thm)],[c_0_3651]) ).

cnf(c_0_3652_0,axiom,
    hAPP(nat,nat,suc,X1) != zero_zero(nat),
    inference(literals_permutation,[status(thm)],[c_0_3652]) ).

cnf(c_0_3653_0,axiom,
    hAPP(nat,nat,suc,X1) != zero_zero(nat),
    inference(literals_permutation,[status(thm)],[c_0_3653]) ).

cnf(c_0_3654_0,axiom,
    hAPP(nat,nat,suc,X1) != zero_zero(nat),
    inference(literals_permutation,[status(thm)],[c_0_3654]) ).

cnf(c_0_3656_0,axiom,
    hAPP(nat,nat,suc,X1) != X1,
    inference(literals_permutation,[status(thm)],[c_0_3656]) ).

cnf(c_0_3657_0,axiom,
    hAPP(nat,nat,suc,X1) != X1,
    inference(literals_permutation,[status(thm)],[c_0_3657]) ).

cnf(c_0_3746_0,axiom,
    b != a,
    inference(literals_permutation,[status(thm)],[c_0_3746]) ).

cnf(c_0_3747_0,axiom,
    d != c,
    inference(literals_permutation,[status(thm)],[c_0_3747]) ).

cnf(c_0_2792_0,axiom,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),e),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))))),
    inference(literals_permutation,[status(thm)],[c_0_2792]) ).

cnf(c_0_2793_0,axiom,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),e)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))))),
    inference(literals_permutation,[status(thm)],[c_0_2793]) ).

cnf(c_0_2794_0,axiom,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))))),
    inference(literals_permutation,[status(thm)],[c_0_2794]) ).

cnf(c_0_2795_0,axiom,
    hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))),arrow_1111136790e_Prof)),
    inference(literals_permutation,[status(thm)],[c_0_2795]) ).

cnf(c_0_2796_0,axiom,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),sk1_esk28_0),one_one(nat))))),lab)),lba)))),
    inference(literals_permutation,[status(thm)],[c_0_2796]) ).

cnf(c_0_2797_0,axiom,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),sk1_esk27_0),one_one(nat))))),lab)),lba)))),
    inference(literals_permutation,[status(thm)],[c_0_2797]) ).

cnf(c_0_2798_0,axiom,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),n),one_one(nat))))),lab)),lba)))),
    inference(literals_permutation,[status(thm)],[c_0_2798]) ).

cnf(c_0_2802_0,axiom,
    hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),X1))),lab)),lba)),arrow_1111136790e_Prof)),
    inference(literals_permutation,[status(thm)],[c_0_2802]) ).

cnf(c_0_2861_0,axiom,
    hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),X1)),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X2))))),
    inference(literals_permutation,[status(thm)],[c_0_2861]) ).

cnf(c_0_2884_0,axiom,
    hBOOL(hAPP(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),f),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_1111136790e_Prof),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_2064824852le_Lin)))),
    inference(literals_permutation,[status(thm)],[c_0_2884]) ).

cnf(c_0_2985_0,axiom,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),p,hAPP(nat,arrow_660593299e_indi,hAPP(fun(arrow_660593299e_indi,nat),fun(nat,arrow_660593299e_indi),hAPP(fun(arrow_660593299e_indi,bool),fun(fun(arrow_660593299e_indi,nat),fun(nat,arrow_660593299e_indi)),hilbert_inv_into(arrow_660593299e_indi,nat),top_top(fun(arrow_660593299e_indi,bool))),h),n)))),
    inference(literals_permutation,[status(thm)],[c_0_2985]) ).

cnf(c_0_3115_0,axiom,
    hBOOL(hAPP(fun(fun(X1,X1),bool),bool,hAPP(fun(X1,X1),fun(fun(fun(X1,X1),bool),bool),member(fun(X1,X1)),combi(X1)),hAPP(fun(X1,fun(X1,bool)),fun(fun(X1,X1),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X1,bool)),fun(fun(X1,X1),bool)),pi(X1,X1),X2),hAPP(fun(X1,bool),fun(X1,fun(X1,bool)),combk(fun(X1,bool),X1),X2)))),
    inference(literals_permutation,[status(thm)],[c_0_3115]) ).

cnf(c_0_3122_0,axiom,
    hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,nat),fun(fun(nat,bool),bool),inj_on(nat,nat),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),X1)),X2)),
    inference(literals_permutation,[status(thm)],[c_0_3122]) ).

cnf(c_0_3123_0,axiom,
    hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),X1)))),
    inference(literals_permutation,[status(thm)],[c_0_3123]) ).

cnf(c_0_3124_0,axiom,
    hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X1)))),
    inference(literals_permutation,[status(thm)],[c_0_3124]) ).

cnf(c_0_3141_0,axiom,
    hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),combb(X3,X2,X1),X4),X5)),top_top(fun(X1,bool))) = hAPP(fun(X3,bool),fun(X2,bool),hAPP(fun(X3,X2),fun(fun(X3,bool),fun(X2,bool)),image(X3,X2),X4),hAPP(fun(X1,bool),fun(X3,bool),hAPP(fun(X1,X3),fun(fun(X1,bool),fun(X3,bool)),image(X1,X3),X5),top_top(fun(X1,bool)))),
    inference(literals_permutation,[status(thm)],[c_0_3141]) ).

cnf(c_0_3149_0,axiom,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),sk1_esk19_0)),
    inference(literals_permutation,[status(thm)],[c_0_3149]) ).

cnf(c_0_3150_0,axiom,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),sk1_esk18_0)),
    inference(literals_permutation,[status(thm)],[c_0_3150]) ).

cnf(c_0_3151_0,axiom,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),b),a)),lba)),
    inference(literals_permutation,[status(thm)],[c_0_3151]) ).

cnf(c_0_3152_0,axiom,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),a),b)),lab)),
    inference(literals_permutation,[status(thm)],[c_0_3152]) ).

cnf(c_0_3153_0,axiom,
    hAPP(fun(X1,bool),fun(X2,bool),hAPP(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool)),image(X1,X2),X3),hAPP(fun(X4,bool),fun(X1,bool),hAPP(fun(X4,X1),fun(fun(X4,bool),fun(X1,bool)),image(X4,X1),X5),X6)) = hAPP(fun(X4,bool),fun(X2,bool),hAPP(fun(X4,X2),fun(fun(X4,bool),fun(X2,bool)),image(X4,X2),hAPP(fun(X4,X1),fun(X4,X2),hAPP(fun(X1,X2),fun(fun(X4,X1),fun(X4,X2)),combb(X1,X2,X4),X3),X5)),X6),
    inference(literals_permutation,[status(thm)],[c_0_3153]) ).

cnf(c_0_3174_0,axiom,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)))),
    inference(literals_permutation,[status(thm)],[c_0_3174]) ).

cnf(c_0_3175_0,axiom,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X1)))),
    inference(literals_permutation,[status(thm)],[c_0_3175]) ).

cnf(c_0_3183_0,axiom,
    hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),hAPP(X2,X1,X3,X4)),hAPP(fun(X2,bool),fun(X1,bool),hAPP(fun(X2,X1),fun(fun(X2,bool),fun(X1,bool)),image(X2,X1),X3),top_top(fun(X2,bool))))),
    inference(literals_permutation,[status(thm)],[c_0_3183]) ).

cnf(c_0_3253_0,axiom,
    hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),bool),member(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),p),arrow_1111136790e_Prof)),
    inference(literals_permutation,[status(thm)],[c_0_3253]) ).

cnf(c_0_3256_0,axiom,
    hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),hAPP(fun(arrow_660593299e_indi,bool),fun(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool)),pi(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),top_top(fun(arrow_660593299e_indi,bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),arrow_660593299e_indi),arrow_2064824852le_Lin)) = arrow_1111136790e_Prof,
    inference(literals_permutation,[status(thm)],[c_0_3256]) ).

cnf(c_0_3266_0,axiom,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),X3) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3)),
    inference(literals_permutation,[status(thm)],[c_0_3266]) ).

cnf(c_0_3272_0,axiom,
    hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),X1))) = hAPP(nat,nat,suc,X1),
    inference(literals_permutation,[status(thm)],[c_0_3272]) ).

cnf(c_0_3284_0,axiom,
    hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X1))) = X1,
    inference(literals_permutation,[status(thm)],[c_0_3284]) ).

cnf(c_0_3342_0,axiom,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2))),
    inference(literals_permutation,[status(thm)],[c_0_3342]) ).

cnf(c_0_3343_0,axiom,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X1))),
    inference(literals_permutation,[status(thm)],[c_0_3343]) ).

cnf(c_0_3345_0,axiom,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X3)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X3)),
    inference(literals_permutation,[status(thm)],[c_0_3345]) ).

cnf(c_0_3353_0,axiom,
    hAPP(X1,X2,hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X1,fun(X3,X2)),fun(fun(X1,X3),fun(X1,X2)),combs(X1,X3,X2),X4),X5),X6) = hAPP(X3,X2,hAPP(X1,fun(X3,X2),X4,X6),hAPP(X1,X3,X5,X6)),
    inference(literals_permutation,[status(thm)],[c_0_3353]) ).

cnf(c_0_3387_0,axiom,
    hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),X1),X2))),
    inference(literals_permutation,[status(thm)],[c_0_3387]) ).

cnf(c_0_3389_0,axiom,
    hAPP(product_prod(X1,X2),X3,hAPP(fun(X1,fun(X2,X3)),fun(product_prod(X1,X2),X3),product_prod_rec(X1,X2,X3),X4),hAPP(X2,product_prod(X1,X2),hAPP(X1,fun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X5),X6)) = hAPP(X2,X3,hAPP(X1,fun(X2,X3),X4,X5),X6),
    inference(literals_permutation,[status(thm)],[c_0_3389]) ).

cnf(c_0_3402_0,axiom,
    hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),sk1_esk66_0),arrow_2064824852le_Lin)),
    inference(literals_permutation,[status(thm)],[c_0_3402]) ).

cnf(c_0_3403_0,axiom,
    hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),sk1_esk19_0),arrow_2064824852le_Lin)),
    inference(literals_permutation,[status(thm)],[c_0_3403]) ).

cnf(c_0_3404_0,axiom,
    hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),sk1_esk18_0),arrow_2064824852le_Lin)),
    inference(literals_permutation,[status(thm)],[c_0_3404]) ).

cnf(c_0_3405_0,axiom,
    hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),lba),arrow_2064824852le_Lin)),
    inference(literals_permutation,[status(thm)],[c_0_3405]) ).

cnf(c_0_3406_0,axiom,
    hBOOL(hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool,hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),bool),member(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),lab),arrow_2064824852le_Lin)),
    inference(literals_permutation,[status(thm)],[c_0_3406]) ).

cnf(c_0_3412_0,axiom,
    hAPP(X1,X2,hAPP(X3,fun(X1,X2),hAPP(fun(X1,fun(X3,X2)),fun(X3,fun(X1,X2)),combc(X1,X3,X2),X4),X5),X6) = hAPP(X3,X2,hAPP(X1,fun(X3,X2),X4,X6),X5),
    inference(literals_permutation,[status(thm)],[c_0_3412]) ).

cnf(c_0_3413_0,axiom,
    hAPP(X1,X2,hAPP(fun(X1,X3),fun(X1,X2),hAPP(fun(X3,X2),fun(fun(X1,X3),fun(X1,X2)),combb(X3,X2,X1),X4),X5),X6) = hAPP(X3,X2,X4,hAPP(X1,X3,X5,X6)),
    inference(literals_permutation,[status(thm)],[c_0_3413]) ).

cnf(c_0_3416_0,axiom,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,X1)),X2) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),
    inference(literals_permutation,[status(thm)],[c_0_3416]) ).

cnf(c_0_3452_0,axiom,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),hAPP(nat,nat,suc,X2)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2)),
    inference(literals_permutation,[status(thm)],[c_0_3452]) ).

cnf(c_0_3453_0,axiom,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,X1)),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),hAPP(nat,nat,suc,X2)),
    inference(literals_permutation,[status(thm)],[c_0_3453]) ).

cnf(c_0_3460_0,axiom,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sk1_esk28_0),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool))))),
    inference(literals_permutation,[status(thm)],[c_0_3460]) ).

cnf(c_0_3461_0,axiom,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),sk1_esk27_0),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool))))),
    inference(literals_permutation,[status(thm)],[c_0_3461]) ).

cnf(c_0_3462_0,axiom,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),n),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool))))),
    inference(literals_permutation,[status(thm)],[c_0_3462]) ).

cnf(c_0_3467_0,axiom,
    hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool)))) = hAPP(fun(arrow_660593299e_indi,bool),fun(nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(fun(arrow_660593299e_indi,bool),fun(nat,bool)),image(arrow_660593299e_indi,nat),sk1_esk100_0),top_top(fun(arrow_660593299e_indi,bool))),
    inference(literals_permutation,[status(thm)],[c_0_3467]) ).

cnf(c_0_3468_0,axiom,
    hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(fun(arrow_660593299e_indi,bool),nat,finite_card(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool)))) = hAPP(fun(arrow_660593299e_indi,bool),fun(nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(fun(arrow_660593299e_indi,bool),fun(nat,bool)),image(arrow_660593299e_indi,nat),h),top_top(fun(arrow_660593299e_indi,bool))),
    inference(literals_permutation,[status(thm)],[c_0_3468]) ).

cnf(c_0_3469_0,axiom,
    hAPP(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool),hAPP(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool)),pi(X1,X2),X3),hAPP(fun(X2,bool),fun(X1,fun(X2,bool)),combk(fun(X2,bool),X1),top_top(fun(X2,bool)))) = top_top(fun(fun(X1,X2),bool)),
    inference(literals_permutation,[status(thm)],[c_0_3469]) ).

cnf(c_0_3490_0,axiom,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,X1))),
    inference(literals_permutation,[status(thm)],[c_0_3490]) ).

cnf(c_0_3494_0,axiom,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X1),hAPP(nat,nat,suc,X1))),
    inference(literals_permutation,[status(thm)],[c_0_3494]) ).

cnf(c_0_3529_0,axiom,
    hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),top_top(fun(X1,bool)))),
    inference(literals_permutation,[status(thm)],[c_0_3529]) ).

cnf(c_0_3530_0,axiom,
    hAPP(X1,X1,hAPP(X1,fun(X1,X1),hAPP(bool,fun(X1,fun(X1,X1)),if(X1),fFalse),X2),X3) = ti(X1,X3),
    inference(literals_permutation,[status(thm)],[c_0_3530]) ).

cnf(c_0_3531_0,axiom,
    hAPP(X1,X1,hAPP(X1,fun(X1,X1),hAPP(bool,fun(X1,fun(X1,X1)),if(X1),fTrue),X2),X3) = ti(X1,X2),
    inference(literals_permutation,[status(thm)],[c_0_3531]) ).

cnf(c_0_3534_0,axiom,
    hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,bool),fun(fun(X1,bool),bool),ord_less_eq(fun(X1,bool)),X2),X2)),
    inference(literals_permutation,[status(thm)],[c_0_3534]) ).

cnf(c_0_3538_0,axiom,
    hBOOL(hAPP(fun(X1,bool),bool,hAPP(fun(X1,X1),fun(fun(X1,bool),bool),inj_on(X1,X1),combi(X1)),X2)),
    inference(literals_permutation,[status(thm)],[c_0_3538]) ).

cnf(c_0_3539_0,axiom,
    hBOOL(hAPP(fun(arrow_660593299e_indi,bool),bool,hAPP(fun(arrow_660593299e_indi,nat),fun(fun(arrow_660593299e_indi,bool),bool),inj_on(arrow_660593299e_indi,nat),sk1_esk100_0),top_top(fun(arrow_660593299e_indi,bool)))),
    inference(literals_permutation,[status(thm)],[c_0_3539]) ).

cnf(c_0_3540_0,axiom,
    hBOOL(hAPP(fun(arrow_660593299e_indi,bool),bool,hAPP(fun(arrow_660593299e_indi,nat),fun(fun(arrow_660593299e_indi,bool),bool),inj_on(arrow_660593299e_indi,nat),h),top_top(fun(arrow_660593299e_indi,bool)))),
    inference(literals_permutation,[status(thm)],[c_0_3540]) ).

cnf(c_0_3542_0,axiom,
    ti(fun(fun(X1,fun(X1,X1)),fun(X1,fun(fun(X2,X1),fun(fun(fun(X2,bool),X1),bool)))),finite908156982e_idem(X1,X2)) = finite908156982e_idem(X1,X2),
    inference(literals_permutation,[status(thm)],[c_0_3542]) ).

cnf(c_0_3543_0,axiom,
    hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),top_top(fun(X1,bool)))),
    inference(literals_permutation,[status(thm)],[c_0_3543]) ).

cnf(c_0_3544_0,axiom,
    hBOOL(hAPP(fun(X1,bool),bool,hAPP(X1,fun(fun(X1,bool),bool),member(X1),X2),top_top(fun(X1,bool)))),
    inference(literals_permutation,[status(thm)],[c_0_3544]) ).

cnf(c_0_3545_0,axiom,
    hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,nat),fun(fun(nat,bool),bool),inj_on(nat,nat),suc),X1)),
    inference(literals_permutation,[status(thm)],[c_0_3545]) ).

cnf(c_0_3570_0,axiom,
    hAPP(fun(X1,bool),fun(sum_sum(X2,X1),bool),hAPP(fun(X2,bool),fun(fun(X1,bool),fun(sum_sum(X2,X1),bool)),sum_Plus(X2,X1),top_top(fun(X2,bool))),top_top(fun(X1,bool))) = top_top(fun(sum_sum(X2,X1),bool)),
    inference(literals_permutation,[status(thm)],[c_0_3570]) ).

cnf(c_0_3575_0,axiom,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),X1)),
    inference(literals_permutation,[status(thm)],[c_0_3575]) ).

cnf(c_0_3576_0,axiom,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),X1)),
    inference(literals_permutation,[status(thm)],[c_0_3576]) ).

cnf(c_0_3583_0,axiom,
    hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X1),X1)),
    inference(literals_permutation,[status(thm)],[c_0_3583]) ).

cnf(c_0_3584_0,axiom,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),X2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X2),X1),
    inference(literals_permutation,[status(thm)],[c_0_3584]) ).

cnf(c_0_3592_0,axiom,
    hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_831799591nimity,f)),
    inference(literals_permutation,[status(thm)],[c_0_3592]) ).

cnf(c_0_3593_0,axiom,
    hBOOL(hAPP(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool,arrow_2037941124le_IIA,f)),
    inference(literals_permutation,[status(thm)],[c_0_3593]) ).

cnf(c_0_3600_0,axiom,
    hAPP(fun(X1,bool),fun(X1,bool),hAPP(fun(X1,X1),fun(fun(X1,bool),fun(X1,bool)),image(X1,X1),combi(X1)),X2) = ti(fun(X1,bool),X2),
    inference(literals_permutation,[status(thm)],[c_0_3600]) ).

cnf(c_0_3602_0,axiom,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),X1) = hAPP(nat,nat,suc,X1),
    inference(literals_permutation,[status(thm)],[c_0_3602]) ).

cnf(c_0_3603_0,axiom,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),one_one(nat)) = hAPP(nat,nat,suc,X1),
    inference(literals_permutation,[status(thm)],[c_0_3603]) ).

cnf(c_0_3604_0,axiom,
    hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X1)) = hAPP(nat,fun(nat,bool),ord_less(nat),X1),
    inference(literals_permutation,[status(thm)],[c_0_3604]) ).

cnf(c_0_3606_0,axiom,
    ti(fun(fun(nat,fun(nat,nat)),fun(fun(X1,nat),fun(nat,fun(fun(X1,bool),nat)))),finite_fold_image(nat,X1)) = finite_fold_image(nat,X1),
    inference(literals_permutation,[status(thm)],[c_0_3606]) ).

cnf(c_0_3607_0,axiom,
    ti(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,bool)),arrow_218898985ctator) = arrow_218898985ctator,
    inference(literals_permutation,[status(thm)],[c_0_3607]) ).

cnf(c_0_3608_0,axiom,
    ti(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),arrow_831799591nimity) = arrow_831799591nimity,
    inference(literals_permutation,[status(thm)],[c_0_3608]) ).

cnf(c_0_3609_0,axiom,
    ti(fun(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),arrow_2037941124le_IIA) = arrow_2037941124le_IIA,
    inference(literals_permutation,[status(thm)],[c_0_3609]) ).

cnf(c_0_3610_0,axiom,
    hAPP(fun(X1,bool),fun(X1,bool),collect(X1),hAPP(bool,fun(X1,bool),combk(bool,X1),fTrue)) = top_top(fun(X1,bool)),
    inference(literals_permutation,[status(thm)],[c_0_3610]) ).

cnf(c_0_3611_0,axiom,
    hAPP(X1,X2,hAPP(X2,fun(X1,X2),combk(X2,X1),X3),X4) = ti(X2,X3),
    inference(literals_permutation,[status(thm)],[c_0_3611]) ).

cnf(c_0_3623_0,axiom,
    ti(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),arrow_1322701812_below) = arrow_1322701812_below,
    inference(literals_permutation,[status(thm)],[c_0_3623]) ).

cnf(c_0_3624_0,axiom,
    ti(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),arrow_14103264_above) = arrow_14103264_above,
    inference(literals_permutation,[status(thm)],[c_0_3624]) ).

cnf(c_0_3626_0,axiom,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),X1) = X1,
    inference(literals_permutation,[status(thm)],[c_0_3626]) ).

cnf(c_0_3627_0,axiom,
    hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X1),zero_zero(nat)) = X1,
    inference(literals_permutation,[status(thm)],[c_0_3627]) ).

cnf(c_0_3631_0,axiom,
    ti(fun(fun(X1,bool),fun(fun(X1,fun(X2,bool)),fun(fun(X1,X2),bool))),pi(X1,X2)) = pi(X1,X2),
    inference(literals_permutation,[status(thm)],[c_0_3631]) ).

cnf(c_0_3632_0,axiom,
    ti(X1,hAPP(X2,X1,X3,X4)) = hAPP(X2,X1,X3,X4),
    inference(literals_permutation,[status(thm)],[c_0_3632]) ).

cnf(c_0_3634_0,axiom,
    hBOOL(hAPP(fun(arrow_660593299e_indi,bool),bool,finite_finite_1(arrow_660593299e_indi),top_top(fun(arrow_660593299e_indi,bool)))),
    inference(literals_permutation,[status(thm)],[c_0_3634]) ).

cnf(c_0_3635_0,axiom,
    ti(fun(fun(X1,fun(X2,X3)),fun(fun(X1,X2),fun(X1,X3))),combs(X1,X2,X3)) = combs(X1,X2,X3),
    inference(literals_permutation,[status(thm)],[c_0_3635]) ).

cnf(c_0_3636_0,axiom,
    hBOOL(hAPP(X1,bool,top_top(fun(X1,bool)),X2)),
    inference(literals_permutation,[status(thm)],[c_0_3636]) ).

cnf(c_0_3637_0,axiom,
    hAPP(X1,X2,ti(fun(X1,X2),X3),X4) = hAPP(X1,X2,X3,X4),
    inference(literals_permutation,[status(thm)],[c_0_3637]) ).

cnf(c_0_3638_0,axiom,
    ti(fun(fun(X1,bool),fun(fun(X2,bool),fun(sum_sum(X1,X2),bool))),sum_Plus(X1,X2)) = sum_Plus(X1,X2),
    inference(literals_permutation,[status(thm)],[c_0_3638]) ).

cnf(c_0_3641_0,axiom,
    hAPP(X1,X2,X3,ti(X1,X4)) = hAPP(X1,X2,X3,X4),
    inference(literals_permutation,[status(thm)],[c_0_3641]) ).

cnf(c_0_3642_0,axiom,
    ti(fun(fun(X1,fun(X2,X3)),fun(product_prod(X1,X2),X3)),product_prod_rec(X1,X2,X3)) = product_prod_rec(X1,X2,X3),
    inference(literals_permutation,[status(thm)],[c_0_3642]) ).

cnf(c_0_3643_0,axiom,
    ti(fun(fun(X1,fun(X2,X3)),fun(X2,fun(X1,X3))),combc(X1,X2,X3)) = combc(X1,X2,X3),
    inference(literals_permutation,[status(thm)],[c_0_3643]) ).

cnf(c_0_3644_0,axiom,
    ti(fun(fun(X1,X2),fun(fun(X3,X1),fun(X3,X2))),combb(X1,X2,X3)) = combb(X1,X2,X3),
    inference(literals_permutation,[status(thm)],[c_0_3644]) ).

cnf(c_0_3647_0,axiom,
    ti(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1427655034_mktop) = arrow_1427655034_mktop,
    inference(literals_permutation,[status(thm)],[c_0_3647]) ).

cnf(c_0_3648_0,axiom,
    ti(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_1278947948_mkbot) = arrow_1278947948_mkbot,
    inference(literals_permutation,[status(thm)],[c_0_3648]) ).

cnf(c_0_3655_0,axiom,
    ti(fun(fun(X1,bool),fun(fun(X1,X2),fun(X2,X1))),hilbert_inv_into(X1,X2)) = hilbert_inv_into(X1,X2),
    inference(literals_permutation,[status(thm)],[c_0_3655]) ).

cnf(c_0_3658_0,axiom,
    ti(fun(fun(product_prod(X1,X2),bool),fun(X1,fun(X2,bool))),in_rel(X1,X2)) = in_rel(X1,X2),
    inference(literals_permutation,[status(thm)],[c_0_3658]) ).

cnf(c_0_3659_0,axiom,
    ti(fun(fun(X1,X2),fun(fun(X1,bool),fun(X2,bool))),image(X1,X2)) = image(X1,X2),
    inference(literals_permutation,[status(thm)],[c_0_3659]) ).

cnf(c_0_3660_0,axiom,
    hAPP(fun(X1,bool),fun(X1,bool),collect(X1),X2) = ti(fun(X1,bool),X2),
    inference(literals_permutation,[status(thm)],[c_0_3660]) ).

cnf(c_0_3661_0,axiom,
    ti(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),bool),arrow_1111136790e_Prof) = arrow_1111136790e_Prof,
    inference(literals_permutation,[status(thm)],[c_0_3661]) ).

cnf(c_0_3662_0,axiom,
    hAPP(fun(product_unit,bool),nat,finite_card(product_unit),top_top(fun(product_unit,bool))) = one_one(nat),
    inference(literals_permutation,[status(thm)],[c_0_3662]) ).

cnf(c_0_3664_0,axiom,
    ti(fun(fun(X1,X2),fun(fun(X1,bool),bool)),inj_on(X1,X2)) = inj_on(X1,X2),
    inference(literals_permutation,[status(thm)],[c_0_3664]) ).

cnf(c_0_3665_0,axiom,
    hAPP(X1,X1,combi(X1),X2) = ti(X1,X2),
    inference(literals_permutation,[status(thm)],[c_0_3665]) ).

cnf(c_0_3668_0,axiom,
    hAPP(nat,nat,suc,zero_zero(nat)) = one_one(nat),
    inference(literals_permutation,[status(thm)],[c_0_3668]) ).

cnf(c_0_3669_0,axiom,
    ti(fun(X1,fun(X2,product_prod(X1,X2))),product_Pair(X1,X2)) = product_Pair(X1,X2),
    inference(literals_permutation,[status(thm)],[c_0_3669]) ).

cnf(c_0_3670_0,axiom,
    ti(fun(bool,fun(X1,fun(X1,X1))),if(X1)) = if(X1),
    inference(literals_permutation,[status(thm)],[c_0_3670]) ).

cnf(c_0_3672_0,axiom,
    ti(fun(X1,fun(fun(X1,bool),bool)),member(X1)) = member(X1),
    inference(literals_permutation,[status(thm)],[c_0_3672]) ).

cnf(c_0_3673_0,axiom,
    ti(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),arrow_2064824852le_Lin) = arrow_2064824852le_Lin,
    inference(literals_permutation,[status(thm)],[c_0_3673]) ).

cnf(c_0_3674_0,axiom,
    ti(fun(fun(X1,bool),fun(X1,bool)),collect(X1)) = collect(X1),
    inference(literals_permutation,[status(thm)],[c_0_3674]) ).

cnf(c_0_3675_0,axiom,
    ti(fun(X1,fun(X2,X1)),combk(X1,X2)) = combk(X1,X2),
    inference(literals_permutation,[status(thm)],[c_0_3675]) ).

cnf(c_0_3681_0,axiom,
    ti(fun(X1,fun(X1,bool)),fequal(X1)) = fequal(X1),
    inference(literals_permutation,[status(thm)],[c_0_3681]) ).

cnf(c_0_3682_0,axiom,
    ti(fun(fun(X1,bool),bool),finite_finite_1(X1)) = finite_finite_1(X1),
    inference(literals_permutation,[status(thm)],[c_0_3682]) ).

cnf(c_0_3683_0,axiom,
    ti(fun(fun(X1,bool),nat),finite_card(X1)) = finite_card(X1),
    inference(literals_permutation,[status(thm)],[c_0_3683]) ).

cnf(c_0_3684_0,axiom,
    ti(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),lba) = lba,
    inference(literals_permutation,[status(thm)],[c_0_3684]) ).

cnf(c_0_3685_0,axiom,
    ti(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),lab) = lab,
    inference(literals_permutation,[status(thm)],[c_0_3685]) ).

cnf(c_0_3686_0,axiom,
    ti(fun(bool,fun(bool,bool)),fdisj) = fdisj,
    inference(literals_permutation,[status(thm)],[c_0_3686]) ).

cnf(c_0_3687_0,axiom,
    ti(fun(bool,fun(bool,bool)),fconj) = fconj,
    inference(literals_permutation,[status(thm)],[c_0_3687]) ).

cnf(c_0_3693_0,axiom,
    ti(X1,ti(X1,X2)) = ti(X1,X2),
    inference(literals_permutation,[status(thm)],[c_0_3693]) ).

cnf(c_0_3694_0,axiom,
    ti(fun(X1,X1),combi(X1)) = combi(X1),
    inference(literals_permutation,[status(thm)],[c_0_3694]) ).

cnf(c_0_3702_0,axiom,
    ti(fun(arrow_660593299e_indi,nat),h) = h,
    inference(literals_permutation,[status(thm)],[c_0_3702]) ).

cnf(c_0_3703_0,axiom,
    ti(fun(bool,bool),fNot) = fNot,
    inference(literals_permutation,[status(thm)],[c_0_3703]) ).

cnf(c_0_3704_0,axiom,
    ti(fun(nat,nat),suc) = suc,
    inference(literals_permutation,[status(thm)],[c_0_3704]) ).

cnf(c_0_3710_0,axiom,
    ti(X1,undefined(X1)) = undefined(X1),
    inference(literals_permutation,[status(thm)],[c_0_3710]) ).

cnf(c_0_3714_0,axiom,
    ti(nat,n) = n,
    inference(literals_permutation,[status(thm)],[c_0_3714]) ).

cnf(c_0_3715_0,axiom,
    ti(arrow_490897120le_alt,e) = e,
    inference(literals_permutation,[status(thm)],[c_0_3715]) ).

cnf(c_0_3716_0,axiom,
    ti(arrow_490897120le_alt,b) = b,
    inference(literals_permutation,[status(thm)],[c_0_3716]) ).

cnf(c_0_3717_0,axiom,
    ti(arrow_490897120le_alt,a) = a,
    inference(literals_permutation,[status(thm)],[c_0_3717]) ).

cnf(c_0_3718_0,axiom,
    ti(bool,fTrue) = fTrue,
    inference(literals_permutation,[status(thm)],[c_0_3718]) ).

cnf(c_0_3719_0,axiom,
    ti(bool,fFalse) = fFalse,
    inference(literals_permutation,[status(thm)],[c_0_3719]) ).

cnf(c_0_3720_0,axiom,
    hBOOL(fTrue),
    inference(literals_permutation,[status(thm)],[c_0_3720]) ).

cnf(c_0_3721_0,axiom,
    finite_finite(product_unit),
    inference(literals_permutation,[status(thm)],[c_0_3721]) ).

cnf(c_0_3722_0,axiom,
    ord(bool),
    inference(literals_permutation,[status(thm)],[c_0_3722]) ).

cnf(c_0_3723_0,axiom,
    top(bool),
    inference(literals_permutation,[status(thm)],[c_0_3723]) ).

cnf(c_0_3724_0,axiom,
    order(bool),
    inference(literals_permutation,[status(thm)],[c_0_3724]) ).

cnf(c_0_3725_0,axiom,
    finite_finite(bool),
    inference(literals_permutation,[status(thm)],[c_0_3725]) ).

cnf(c_0_3726_0,axiom,
    preorder(bool),
    inference(literals_permutation,[status(thm)],[c_0_3726]) ).

cnf(c_0_3727_0,axiom,
    one(nat),
    inference(literals_permutation,[status(thm)],[c_0_3727]) ).

cnf(c_0_3728_0,axiom,
    zero(nat),
    inference(literals_permutation,[status(thm)],[c_0_3728]) ).

cnf(c_0_3729_0,axiom,
    ord(nat),
    inference(literals_permutation,[status(thm)],[c_0_3729]) ).

cnf(c_0_3730_0,axiom,
    order(nat),
    inference(literals_permutation,[status(thm)],[c_0_3730]) ).

cnf(c_0_3731_0,axiom,
    monoid_add(nat),
    inference(literals_permutation,[status(thm)],[c_0_3731]) ).

cnf(c_0_3732_0,axiom,
    linorder(nat),
    inference(literals_permutation,[status(thm)],[c_0_3732]) ).

cnf(c_0_3733_0,axiom,
    preorder(nat),
    inference(literals_permutation,[status(thm)],[c_0_3733]) ).

cnf(c_0_3734_0,axiom,
    zero_neq_one(nat),
    inference(literals_permutation,[status(thm)],[c_0_3734]) ).

cnf(c_0_3735_0,axiom,
    comm_semiring_1(nat),
    inference(literals_permutation,[status(thm)],[c_0_3735]) ).

cnf(c_0_3736_0,axiom,
    comm_monoid_add(nat),
    inference(literals_permutation,[status(thm)],[c_0_3736]) ).

cnf(c_0_3737_0,axiom,
    ab_semigroup_add(nat),
    inference(literals_permutation,[status(thm)],[c_0_3737]) ).

cnf(c_0_3738_0,axiom,
    linordered_semidom(nat),
    inference(literals_permutation,[status(thm)],[c_0_3738]) ).

cnf(c_0_3739_0,axiom,
    cancel_semigroup_add(nat),
    inference(literals_permutation,[status(thm)],[c_0_3739]) ).

cnf(c_0_3740_0,axiom,
    cancel146912293up_add(nat),
    inference(literals_permutation,[status(thm)],[c_0_3740]) ).

cnf(c_0_3741_0,axiom,
    ordere216010020id_add(nat),
    inference(literals_permutation,[status(thm)],[c_0_3741]) ).

cnf(c_0_3742_0,axiom,
    ordere779506340up_add(nat),
    inference(literals_permutation,[status(thm)],[c_0_3742]) ).

cnf(c_0_3743_0,axiom,
    ordere236663937imp_le(nat),
    inference(literals_permutation,[status(thm)],[c_0_3743]) ).

cnf(c_0_3744_0,axiom,
    ordere223160158up_add(nat),
    inference(literals_permutation,[status(thm)],[c_0_3744]) ).

cnf(c_0_3745_0,axiom,
    semiri456707255roduct(nat),
    inference(literals_permutation,[status(thm)],[c_0_3745]) ).

% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_001,conjecture,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,p))),
    file('<stdin>',conj_0) ).

fof(c_0_1_002,hypothesis,
    ti(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),f) = f,
    file('<stdin>',tsy_v_F_res) ).

fof(c_0_2_003,hypothesis,
    ti(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),p) = p,
    file('<stdin>',tsy_v_P_____res) ).

fof(c_0_3_004,hypothesis,
    ! [X1] :
      ( hBOOL(ti(bool,X1))
    <=> hBOOL(X1) ),
    file('<stdin>',tsy_c_hBOOL_arg1) ).

fof(c_0_4_005,hypothesis,
    ti(arrow_490897120le_alt,d) = d,
    file('<stdin>',tsy_v_d_____res) ).

fof(c_0_5_006,hypothesis,
    ti(arrow_490897120le_alt,c) = c,
    file('<stdin>',tsy_v_c_____res) ).

fof(c_0_6_007,negated_conjecture,
    ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,p))),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[c_0_0])]) ).

fof(c_0_7_008,hypothesis,
    ti(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),f) = f,
    c_0_1 ).

fof(c_0_8_009,hypothesis,
    ti(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),p) = p,
    c_0_2 ).

fof(c_0_9_010,hypothesis,
    ! [X1] :
      ( hBOOL(ti(bool,X1))
    <=> hBOOL(X1) ),
    c_0_3 ).

fof(c_0_10_011,hypothesis,
    ti(arrow_490897120le_alt,d) = d,
    c_0_4 ).

fof(c_0_11_012,hypothesis,
    ti(arrow_490897120le_alt,c) = c,
    c_0_5 ).

fof(c_0_12_013,negated_conjecture,
    ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,p))),
    c_0_6 ).

fof(c_0_13_014,hypothesis,
    ti(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),f) = f,
    c_0_7 ).

fof(c_0_14_015,hypothesis,
    ti(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),p) = p,
    c_0_8 ).

fof(c_0_15_016,hypothesis,
    ! [X2,X3] :
      ( ( ~ hBOOL(ti(bool,X2))
        | hBOOL(X2) )
      & ( ~ hBOOL(X3)
        | hBOOL(ti(bool,X3)) ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])]) ).

fof(c_0_16_017,hypothesis,
    ti(arrow_490897120le_alt,d) = d,
    c_0_10 ).

fof(c_0_17_018,hypothesis,
    ti(arrow_490897120le_alt,c) = c,
    c_0_11 ).

cnf(c_0_18_019,negated_conjecture,
    ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,p))),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_19_020,hypothesis,
    ti(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),f) = f,
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_20_021,hypothesis,
    ti(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),p) = p,
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_21_022,hypothesis,
    ( hBOOL(X1)
    | ~ hBOOL(ti(bool,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_22_023,hypothesis,
    ( hBOOL(ti(bool,X1))
    | ~ hBOOL(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_23_024,hypothesis,
    ti(arrow_490897120le_alt,d) = d,
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_24_025,hypothesis,
    ti(arrow_490897120le_alt,c) = c,
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_25_026,negated_conjecture,
    ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,p))),
    c_0_18,
    [final] ).

cnf(c_0_26_027,hypothesis,
    ti(fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),f) = f,
    c_0_19,
    [final] ).

cnf(c_0_27_028,hypothesis,
    ti(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),p) = p,
    c_0_20,
    [final] ).

cnf(c_0_28_029,hypothesis,
    ( hBOOL(X1)
    | ~ hBOOL(ti(bool,X1)) ),
    c_0_21,
    [final] ).

cnf(c_0_29_030,hypothesis,
    ( hBOOL(ti(bool,X1))
    | ~ hBOOL(X1) ),
    c_0_22,
    [final] ).

cnf(c_0_30_031,hypothesis,
    ti(arrow_490897120le_alt,d) = d,
    c_0_23,
    [final] ).

cnf(c_0_31_032,hypothesis,
    ti(arrow_490897120le_alt,c) = c,
    c_0_24,
    [final] ).

% End CNF derivation

%-------------------------------------------------------------
% Proof by iprover

cnf(c_155,plain,
    hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e)))))),
    file('/export/starexec/sandbox/tmp/iprover_modulo_3bccca.p',c_0_2794_0) ).

cnf(c_2800,plain,
    ( ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),ord_less(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1427655034_mktop),p)),e))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combs(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,bool),fun(arrow_660593299e_indi,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(bool,fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),if(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(nat,fun(arrow_660593299e_indi,bool),hAPP(fun(arrow_660593299e_indi,fun(nat,bool)),fun(nat,fun(arrow_660593299e_indi,bool)),combc(arrow_660593299e_indi,nat,bool),hAPP(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(arrow_660593299e_indi,nat),fun(arrow_660593299e_indi,fun(nat,bool))),combb(nat,fun(nat,bool),arrow_660593299e_indi),fequal(nat)),h)),n))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),arrow_660593299e_indi),arrow_14103264_above),p)),c)),e))),hAPP(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(arrow_490897120le_alt,fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),combc(arrow_660593299e_indi,arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),hAPP(fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool))),fun(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(arrow_660593299e_indi,fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)))),combb(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),fun(arrow_490897120le_alt,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),arrow_660593299e_indi),arrow_1278947948_mkbot),p)),e))))))
    | hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,p))) ),
    file('/export/starexec/sandbox/tmp/iprover_modulo_3bccca.p',c_0_2788_0) ).

cnf(c_2807,negated_conjecture,
    ~ hBOOL(hAPP(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool,hAPP(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),fun(fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),bool),member(product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),hAPP(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt),hAPP(arrow_490897120le_alt,fun(arrow_490897120le_alt,product_prod(arrow_490897120le_alt,arrow_490897120le_alt)),product_Pair(arrow_490897120le_alt,arrow_490897120le_alt),c),d)),hAPP(fun(arrow_660593299e_indi,fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool)),fun(product_prod(arrow_490897120le_alt,arrow_490897120le_alt),bool),f,p))),
    file('/export/starexec/sandbox/tmp/iprover_modulo_3bccca.p',c_0_25) ).

cnf(contradiction,plain,
    $false,
    inference(minisat,[status(thm)],[c_155,c_2800,c_2807]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11  % Problem  : SCT171+6 : TPTP v8.1.0. Released v5.3.0.
% 0.07/0.12  % Command  : iprover_modulo %s %d
% 0.12/0.33  % Computer : n027.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Fri Jul  1 21:55:38 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.34  % Running in mono-core mode
% 0.67/0.85  % Orienting using strategy Equiv(ClausalAll)
% 0.67/0.85  % FOF problem with conjecture
% 0.67/0.85  % Executing iprover_moduloopt --modulo true --schedule none --sub_typing false --res_to_prop_solver none --res_prop_simpl_given false --res_lit_sel kbo_max --large_theory_mode false --res_time_limit 1000 --res_orphan_elimination false --prep_sem_filter none --prep_unflatten false --comb_res_mult 1000 --comb_inst_mult 300 --clausifier .//eprover --clausifier_options "--tstp-format  " --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_43c944.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox/tmp/iprover_modulo_3bccca.p | tee /export/starexec/sandbox/tmp/iprover_modulo_out_528549 | grep -v "SZS"
% 0.67/0.87  
% 0.67/0.87  %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.67/0.87  
% 0.67/0.87  % 
% 0.67/0.87  % ------  iProver source info 
% 0.67/0.87  
% 0.67/0.87  % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.67/0.87  % git: non_committed_changes: true
% 0.67/0.87  % git: last_make_outside_of_git: true
% 0.67/0.87  
% 0.67/0.87  % 
% 0.67/0.87  % ------ Input Options
% 0.67/0.87  
% 0.67/0.87  % --out_options                         all
% 0.67/0.87  % --tptp_safe_out                       true
% 0.67/0.87  % --problem_path                        ""
% 0.67/0.87  % --include_path                        ""
% 0.67/0.87  % --clausifier                          .//eprover
% 0.67/0.87  % --clausifier_options                  --tstp-format  
% 0.67/0.87  % --stdin                               false
% 0.67/0.87  % --dbg_backtrace                       false
% 0.67/0.87  % --dbg_dump_prop_clauses               false
% 0.67/0.87  % --dbg_dump_prop_clauses_file          -
% 0.67/0.87  % --dbg_out_stat                        false
% 0.67/0.87  
% 0.67/0.87  % ------ General Options
% 0.67/0.87  
% 0.67/0.87  % --fof                                 false
% 0.67/0.87  % --time_out_real                       150.
% 0.67/0.87  % --time_out_prep_mult                  0.2
% 0.67/0.87  % --time_out_virtual                    -1.
% 0.67/0.87  % --schedule                            none
% 0.67/0.87  % --ground_splitting                    input
% 0.67/0.87  % --splitting_nvd                       16
% 0.67/0.87  % --non_eq_to_eq                        false
% 0.67/0.87  % --prep_gs_sim                         true
% 0.67/0.87  % --prep_unflatten                      false
% 0.67/0.87  % --prep_res_sim                        true
% 0.67/0.87  % --prep_upred                          true
% 0.67/0.87  % --res_sim_input                       true
% 0.67/0.87  % --clause_weak_htbl                    true
% 0.67/0.87  % --gc_record_bc_elim                   false
% 0.67/0.87  % --symbol_type_check                   false
% 0.67/0.87  % --clausify_out                        false
% 0.67/0.87  % --large_theory_mode                   false
% 0.67/0.87  % --prep_sem_filter                     none
% 0.67/0.87  % --prep_sem_filter_out                 false
% 0.67/0.87  % --preprocessed_out                    false
% 0.67/0.87  % --sub_typing                          false
% 0.67/0.87  % --brand_transform                     false
% 0.67/0.87  % --pure_diseq_elim                     true
% 0.67/0.87  % --min_unsat_core                      false
% 0.67/0.87  % --pred_elim                           true
% 0.67/0.87  % --add_important_lit                   false
% 0.67/0.87  % --soft_assumptions                    false
% 0.67/0.87  % --reset_solvers                       false
% 0.67/0.87  % --bc_imp_inh                          []
% 0.67/0.87  % --conj_cone_tolerance                 1.5
% 0.67/0.87  % --prolific_symb_bound                 500
% 0.67/0.87  % --lt_threshold                        2000
% 0.67/0.87  
% 0.67/0.87  % ------ SAT Options
% 0.67/0.87  
% 0.67/0.87  % --sat_mode                            false
% 0.67/0.87  % --sat_fm_restart_options              ""
% 0.67/0.87  % --sat_gr_def                          false
% 0.67/0.87  % --sat_epr_types                       true
% 0.67/0.87  % --sat_non_cyclic_types                false
% 0.67/0.87  % --sat_finite_models                   false
% 0.67/0.87  % --sat_fm_lemmas                       false
% 0.67/0.87  % --sat_fm_prep                         false
% 0.67/0.87  % --sat_fm_uc_incr                      true
% 0.67/0.87  % --sat_out_model                       small
% 0.67/0.87  % --sat_out_clauses                     false
% 0.67/0.87  
% 0.67/0.87  % ------ QBF Options
% 0.67/0.87  
% 0.67/0.87  % --qbf_mode                            false
% 0.67/0.87  % --qbf_elim_univ                       true
% 0.67/0.87  % --qbf_sk_in                           true
% 0.67/0.87  % --qbf_pred_elim                       true
% 0.67/0.87  % --qbf_split                           32
% 0.67/0.87  
% 0.67/0.87  % ------ BMC1 Options
% 0.67/0.87  
% 0.67/0.87  % --bmc1_incremental                    false
% 0.67/0.87  % --bmc1_axioms                         reachable_all
% 0.67/0.87  % --bmc1_min_bound                      0
% 0.67/0.87  % --bmc1_max_bound                      -1
% 0.67/0.87  % --bmc1_max_bound_default              -1
% 0.67/0.87  % --bmc1_symbol_reachability            true
% 0.67/0.87  % --bmc1_property_lemmas                false
% 0.67/0.87  % --bmc1_k_induction                    false
% 0.67/0.87  % --bmc1_non_equiv_states               false
% 0.67/0.87  % --bmc1_deadlock                       false
% 0.67/0.87  % --bmc1_ucm                            false
% 0.67/0.87  % --bmc1_add_unsat_core                 none
% 0.67/0.87  % --bmc1_unsat_core_children            false
% 0.67/0.87  % --bmc1_unsat_core_extrapolate_axioms  false
% 0.67/0.87  % --bmc1_out_stat                       full
% 0.67/0.87  % --bmc1_ground_init                    false
% 0.67/0.87  % --bmc1_pre_inst_next_state            false
% 0.67/0.87  % --bmc1_pre_inst_state                 false
% 0.67/0.87  % --bmc1_pre_inst_reach_state           false
% 0.67/0.87  % --bmc1_out_unsat_core                 false
% 0.67/0.87  % --bmc1_aig_witness_out                false
% 0.67/0.87  % --bmc1_verbose                        false
% 0.67/0.87  % --bmc1_dump_clauses_tptp              false
% 0.70/0.99  % --bmc1_dump_unsat_core_tptp           false
% 0.70/0.99  % --bmc1_dump_file                      -
% 0.70/0.99  % --bmc1_ucm_expand_uc_limit            128
% 0.70/0.99  % --bmc1_ucm_n_expand_iterations        6
% 0.70/0.99  % --bmc1_ucm_extend_mode                1
% 0.70/0.99  % --bmc1_ucm_init_mode                  2
% 0.70/0.99  % --bmc1_ucm_cone_mode                  none
% 0.70/0.99  % --bmc1_ucm_reduced_relation_type      0
% 0.70/0.99  % --bmc1_ucm_relax_model                4
% 0.70/0.99  % --bmc1_ucm_full_tr_after_sat          true
% 0.70/0.99  % --bmc1_ucm_expand_neg_assumptions     false
% 0.70/0.99  % --bmc1_ucm_layered_model              none
% 0.70/0.99  % --bmc1_ucm_max_lemma_size             10
% 0.70/0.99  
% 0.70/0.99  % ------ AIG Options
% 0.70/0.99  
% 0.70/0.99  % --aig_mode                            false
% 0.70/0.99  
% 0.70/0.99  % ------ Instantiation Options
% 0.70/0.99  
% 0.70/0.99  % --instantiation_flag                  true
% 0.70/0.99  % --inst_lit_sel                        [+prop;+sign;+ground;-num_var;-num_symb]
% 0.70/0.99  % --inst_solver_per_active              750
% 0.70/0.99  % --inst_solver_calls_frac              0.5
% 0.70/0.99  % --inst_passive_queue_type             priority_queues
% 0.70/0.99  % --inst_passive_queues                 [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.70/0.99  % --inst_passive_queues_freq            [25;2]
% 0.70/0.99  % --inst_dismatching                    true
% 0.70/0.99  % --inst_eager_unprocessed_to_passive   true
% 0.70/0.99  % --inst_prop_sim_given                 true
% 0.70/0.99  % --inst_prop_sim_new                   false
% 0.70/0.99  % --inst_orphan_elimination             true
% 0.70/0.99  % --inst_learning_loop_flag             true
% 0.70/0.99  % --inst_learning_start                 3000
% 0.70/0.99  % --inst_learning_factor                2
% 0.70/0.99  % --inst_start_prop_sim_after_learn     3
% 0.70/0.99  % --inst_sel_renew                      solver
% 0.70/0.99  % --inst_lit_activity_flag              true
% 0.70/0.99  % --inst_out_proof                      true
% 0.70/0.99  
% 0.70/0.99  % ------ Resolution Options
% 0.70/0.99  
% 0.70/0.99  % --resolution_flag                     true
% 0.70/0.99  % --res_lit_sel                         kbo_max
% 0.70/0.99  % --res_to_prop_solver                  none
% 0.70/0.99  % --res_prop_simpl_new                  false
% 0.70/0.99  % --res_prop_simpl_given                false
% 0.70/0.99  % --res_passive_queue_type              priority_queues
% 0.70/0.99  % --res_passive_queues                  [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 0.70/0.99  % --res_passive_queues_freq             [15;5]
% 0.70/0.99  % --res_forward_subs                    full
% 0.70/0.99  % --res_backward_subs                   full
% 0.70/0.99  % --res_forward_subs_resolution         true
% 0.70/0.99  % --res_backward_subs_resolution        true
% 0.70/0.99  % --res_orphan_elimination              false
% 0.70/0.99  % --res_time_limit                      1000.
% 0.70/0.99  % --res_out_proof                       true
% 0.70/0.99  % --proof_out_file                      /export/starexec/sandbox/tmp/iprover_proof_43c944.s
% 0.70/0.99  % --modulo                              true
% 0.70/0.99  
% 0.70/0.99  % ------ Combination Options
% 0.70/0.99  
% 0.70/0.99  % --comb_res_mult                       1000
% 0.70/0.99  % --comb_inst_mult                      300
% 0.70/0.99  % ------ 
% 0.70/0.99  
% 0.70/0.99  % ------ Parsing...% 
% 0.70/0.99  
% 0.70/0.99  
% 0.70/0.99  % ------                             Statistics
% 0.70/0.99  
% 0.70/0.99  % ------ General
% 0.70/0.99  
% 0.70/0.99  % num_of_input_clauses:                 730
% 0.70/0.99  % num_of_input_neg_conjectures:         0
% 0.70/0.99  % num_of_splits:                        0
% 0.70/0.99  % num_of_split_atoms:                   0
% 0.70/0.99  % num_of_sem_filtered_clauses:          0
% 0.70/0.99  % num_of_subtypes:                      0
% 0.70/0.99  % monotx_restored_types:                0
% 0.70/0.99  % sat_num_of_epr_types:                 0
% 0.70/0.99  % sat_num_of_non_cyclic_types:          0
% 0.70/0.99  % sat_guarded_non_collapsed_types:      0
% 0.70/0.99  % is_epr:                               0
% 0.70/0.99  % is_horn:                              0
% 0.70/0.99  % has_eq:                               0
% 0.70/0.99  % num_pure_diseq_elim:                  0
% 0.70/0.99  % simp_replaced_by:                     0
% 0.70/0.99  % res_preprocessed:                     0
% 0.70/0.99  % prep_upred:                           0
% 0.70/0.99  % prep_unflattend:                      0
% 0.70/0.99  % pred_elim_cands:                      0
% 0.70/0.99  % pred_elim:                            0
% 0.70/0.99  % pred_elim_cl:                         0
% 0.70/0.99  % pred_elim_cycles:                     0
% 0.70/0.99  % forced_gc_time:                       0
% 0.70/0.99  % gc_basic_clause_elim:                 0
% 0.70/0.99  % parsing_time:                         0.
% 0.70/0.99  % sem_filter_time:                      0.
% 0.70/0.99  % pred_elim_time:                       0.
% 0.70/0.99  % out_proof_time:                       0.
% 0.70/0.99  % monotx_time:                          0.
% 0.70/0.99  % subtype_inf_time:                     0.
% 0.70/0.99  % unif_index_cands_time:                0.
% 0.70/0.99  % uFatal error: exception Failure("Parse error in: /export/starexec/sandbox/tmp/iprover_modulo_3bccca.p line: 733 near token: '!='")
% 0.70/0.99  nif_index_add_time:                  0.
% 0.70/0.99  % total_time:                           0.132
% 0.70/0.99  % num_of_symbols:                       146
% 0.70/0.99  % num_of_terms:                         1827
% 0.70/0.99  
% 0.70/0.99  % ------ Propositional Solver
% 0.70/0.99  
% 0.70/0.99  % prop_solver_calls:                    0
% 0.70/0.99  % prop_fast_solver_calls:               0
% 0.70/0.99  % prop_num_of_clauses:                  0
% 0.70/0.99  % prop_preprocess_simplified:           0
% 0.70/0.99  % prop_fo_subsumed:                     0
% 0.70/0.99  % prop_solver_time:                     0.
% 0.70/0.99  % prop_fast_solver_time:                0.
% 0.70/0.99  % prop_unsat_core_time:                 0.
% 0.70/0.99  
% 0.70/0.99  % ------ QBF 
% 0.70/0.99  
% 0.70/0.99  % qbf_q_res:                            0
% 0.70/0.99  % qbf_num_tautologies:                  0
% 0.70/0.99  % qbf_prep_cycles:                      0
% 0.70/0.99  
% 0.70/0.99  % ------ BMC1
% 0.70/0.99  
% 0.70/0.99  % bmc1_current_bound:                   -1
% 0.70/0.99  % bmc1_last_solved_bound:               -1
% 0.70/0.99  % bmc1_unsat_core_size:                 -1
% 0.70/0.99  % bmc1_unsat_core_parents_size:         -1
% 0.70/0.99  % bmc1_merge_next_fun:                  0
% 0.70/0.99  % bmc1_unsat_core_clauses_time:         0.
% 0.70/0.99  
% 0.70/0.99  % ------ Instantiation
% 0.70/0.99  
% 0.70/0.99  % inst_num_of_clauses:                  undef
% 0.70/0.99  % inst_num_in_passive:                  undef
% 0.70/0.99  % inst_num_in_active:                   0
% 0.70/0.99  % inst_num_in_unprocessed:              0
% 0.70/0.99  % inst_num_of_loops:                    0
% 0.70/0.99  % inst_num_of_learning_restarts:        0
% 0.70/0.99  % inst_num_moves_active_passive:        0
% 0.70/0.99  % inst_lit_activity:                    0
% 0.70/0.99  % inst_lit_activity_moves:              0
% 0.70/0.99  % inst_num_tautologies:                 0
% 0.70/0.99  % inst_num_prop_implied:                0
% 0.70/0.99  % inst_num_existing_simplified:         0
% 0.70/0.99  % inst_num_eq_res_simplified:           0
% 0.70/0.99  % inst_num_child_elim:                  0
% 0.70/0.99  % inst_num_of_dismatching_blockings:    0
% 0.70/0.99  % inst_num_of_non_proper_insts:         0
% 0.70/0.99  % inst_num_of_duplicates:               0
% 0.70/0.99  % inst_inst_num_from_inst_to_res:       0
% 0.70/0.99  % inst_dismatching_checking_time:       0.
% 0.70/0.99  
% 0.70/0.99  % ------ Resolution
% 0.70/0.99  
% 0.70/0.99  % res_num_of_clauses:                   undef
% 0.70/0.99  % res_num_in_passive:                   undef
% 0.70/0.99  % res_num_in_active:                    0
% 0.70/0.99  % res_num_of_loops:                     0
% 0.70/0.99  % res_forward_subset_subsumed:          0
% 0.70/0.99  % res_backward_subset_subsumed:         0
% 0.70/0.99  % res_forward_subsumed:                 0
% 0.70/0.99  % res_backward_subsumed:                0
% 0.70/0.99  % res_forward_subsumption_resolution:   0
% 0.70/0.99  % res_backward_subsumption_resolution:  0
% 0.70/0.99  % res_clause_to_clause_subsumption:     0
% 0.70/0.99  % res_orphan_elimination:               0
% 0.70/0.99  % res_tautology_del:                    0
% 0.70/0.99  % res_num_eq_res_simplified:            0
% 0.70/0.99  % res_num_sel_changes:                  0
% 0.70/0.99  % res_moves_from_active_to_pass:        0
% 0.70/0.99  
% 0.70/0.99  % Status Unknown
% 1.22/1.38  % Orienting using strategy ClausalAll
% 1.22/1.38  % FOF problem with conjecture
% 1.22/1.38  % Executing iprover_moduloopt --modulo true --schedule none --sub_typing false --res_to_prop_solver none --res_prop_simpl_given false --res_lit_sel kbo_max --large_theory_mode false --res_time_limit 1000 --res_orphan_elimination false --prep_sem_filter none --prep_unflatten false --comb_res_mult 1000 --comb_inst_mult 300 --clausifier .//eprover --clausifier_options "--tstp-format  " --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_43c944.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox/tmp/iprover_modulo_3bccca.p | tee /export/starexec/sandbox/tmp/iprover_modulo_out_1288d6 | grep -v "SZS"
% 1.22/1.39  
% 1.22/1.39  %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 1.22/1.39  
% 1.22/1.39  % 
% 1.22/1.39  % ------  iProver source info 
% 1.22/1.39  
% 1.22/1.39  % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 1.22/1.39  % git: non_committed_changes: true
% 1.22/1.39  % git: last_make_outside_of_git: true
% 1.22/1.39  
% 1.22/1.39  % 
% 1.22/1.39  % ------ Input Options
% 1.22/1.39  
% 1.22/1.39  % --out_options                         all
% 1.22/1.39  % --tptp_safe_out                       true
% 1.22/1.39  % --problem_path                        ""
% 1.22/1.39  % --include_path                        ""
% 1.22/1.39  % --clausifier                          .//eprover
% 1.22/1.39  % --clausifier_options                  --tstp-format  
% 1.22/1.39  % --stdin                               false
% 1.22/1.39  % --dbg_backtrace                       false
% 1.22/1.39  % --dbg_dump_prop_clauses               false
% 1.22/1.39  % --dbg_dump_prop_clauses_file          -
% 1.22/1.39  % --dbg_out_stat                        false
% 1.22/1.39  
% 1.22/1.39  % ------ General Options
% 1.22/1.39  
% 1.22/1.39  % --fof                                 false
% 1.22/1.39  % --time_out_real                       150.
% 1.22/1.39  % --time_out_prep_mult                  0.2
% 1.22/1.39  % --time_out_virtual                    -1.
% 1.22/1.39  % --schedule                            none
% 1.22/1.39  % --ground_splitting                    input
% 1.22/1.39  % --splitting_nvd                       16
% 1.22/1.39  % --non_eq_to_eq                        false
% 1.22/1.39  % --prep_gs_sim                         true
% 1.22/1.39  % --prep_unflatten                      false
% 1.22/1.39  % --prep_res_sim                        true
% 1.22/1.39  % --prep_upred                          true
% 1.22/1.39  % --res_sim_input                       true
% 1.22/1.39  % --clause_weak_htbl                    true
% 1.22/1.39  % --gc_record_bc_elim                   false
% 1.22/1.39  % --symbol_type_check                   false
% 1.22/1.39  % --clausify_out                        false
% 1.22/1.39  % --large_theory_mode                   false
% 1.22/1.39  % --prep_sem_filter                     none
% 1.22/1.39  % --prep_sem_filter_out                 false
% 1.22/1.39  % --preprocessed_out                    false
% 1.22/1.39  % --sub_typing                          false
% 1.22/1.39  % --brand_transform                     false
% 1.22/1.39  % --pure_diseq_elim                     true
% 1.22/1.39  % --min_unsat_core                      false
% 1.22/1.39  % --pred_elim                           true
% 1.22/1.39  % --add_important_lit                   false
% 1.22/1.39  % --soft_assumptions                    false
% 1.22/1.39  % --reset_solvers                       false
% 1.22/1.39  % --bc_imp_inh                          []
% 1.22/1.39  % --conj_cone_tolerance                 1.5
% 1.22/1.39  % --prolific_symb_bound                 500
% 1.22/1.39  % --lt_threshold                        2000
% 1.22/1.39  
% 1.22/1.39  % ------ SAT Options
% 1.22/1.39  
% 1.22/1.39  % --sat_mode                            false
% 1.22/1.39  % --sat_fm_restart_options              ""
% 1.22/1.39  % --sat_gr_def                          false
% 1.22/1.39  % --sat_epr_types                       true
% 1.22/1.39  % --sat_non_cyclic_types                false
% 1.22/1.39  % --sat_finite_models                   false
% 1.22/1.39  % --sat_fm_lemmas                       false
% 1.22/1.39  % --sat_fm_prep                         false
% 1.22/1.39  % --sat_fm_uc_incr                      true
% 1.22/1.39  % --sat_out_model                       small
% 1.22/1.39  % --sat_out_clauses                     false
% 1.22/1.39  
% 1.22/1.39  % ------ QBF Options
% 1.22/1.39  
% 1.22/1.39  % --qbf_mode                            false
% 1.22/1.39  % --qbf_elim_univ                       true
% 1.22/1.39  % --qbf_sk_in                           true
% 1.22/1.39  % --qbf_pred_elim                       true
% 1.22/1.39  % --qbf_split                           32
% 1.22/1.39  
% 1.22/1.39  % ------ BMC1 Options
% 1.22/1.39  
% 1.22/1.39  % --bmc1_incremental                    false
% 1.22/1.39  % --bmc1_axioms                         reachable_all
% 1.22/1.39  % --bmc1_min_bound                      0
% 1.22/1.39  % --bmc1_max_bound                      -1
% 1.22/1.39  % --bmc1_max_bound_default              -1
% 1.22/1.39  % --bmc1_symbol_reachability            true
% 1.22/1.39  % --bmc1_property_lemmas                false
% 1.22/1.39  % --bmc1_k_induction                    false
% 1.22/1.39  % --bmc1_non_equiv_states               false
% 1.22/1.39  % --bmc1_deadlock                       false
% 1.22/1.39  % --bmc1_ucm                            false
% 1.22/1.39  % --bmc1_add_unsat_core                 none
% 1.22/1.39  % --bmc1_unsat_core_children            false
% 1.22/1.39  % --bmc1_unsat_core_extrapolate_axioms  false
% 1.22/1.39  % --bmc1_out_stat                       full
% 1.22/1.39  % --bmc1_ground_init                    false
% 1.22/1.39  % --bmc1_pre_inst_next_state            false
% 1.22/1.39  % --bmc1_pre_inst_state                 false
% 1.22/1.39  % --bmc1_pre_inst_reach_state           false
% 1.22/1.39  % --bmc1_out_unsat_core                 false
% 1.22/1.39  % --bmc1_aig_witness_out                false
% 1.22/1.39  % --bmc1_verbose                        false
% 1.22/1.39  % --bmc1_dump_clauses_tptp              false
% 1.61/1.79  % --bmc1_dump_unsat_core_tptp           false
% 1.61/1.79  % --bmc1_dump_file                      -
% 1.61/1.79  % --bmc1_ucm_expand_uc_limit            128
% 1.61/1.79  % --bmc1_ucm_n_expand_iterations        6
% 1.61/1.79  % --bmc1_ucm_extend_mode                1
% 1.61/1.79  % --bmc1_ucm_init_mode                  2
% 1.61/1.79  % --bmc1_ucm_cone_mode                  none
% 1.61/1.79  % --bmc1_ucm_reduced_relation_type      0
% 1.61/1.79  % --bmc1_ucm_relax_model                4
% 1.61/1.79  % --bmc1_ucm_full_tr_after_sat          true
% 1.61/1.79  % --bmc1_ucm_expand_neg_assumptions     false
% 1.61/1.79  % --bmc1_ucm_layered_model              none
% 1.61/1.79  % --bmc1_ucm_max_lemma_size             10
% 1.61/1.79  
% 1.61/1.79  % ------ AIG Options
% 1.61/1.79  
% 1.61/1.79  % --aig_mode                            false
% 1.61/1.79  
% 1.61/1.79  % ------ Instantiation Options
% 1.61/1.79  
% 1.61/1.79  % --instantiation_flag                  true
% 1.61/1.79  % --inst_lit_sel                        [+prop;+sign;+ground;-num_var;-num_symb]
% 1.61/1.79  % --inst_solver_per_active              750
% 1.61/1.79  % --inst_solver_calls_frac              0.5
% 1.61/1.79  % --inst_passive_queue_type             priority_queues
% 1.61/1.79  % --inst_passive_queues                 [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 1.61/1.79  % --inst_passive_queues_freq            [25;2]
% 1.61/1.79  % --inst_dismatching                    true
% 1.61/1.79  % --inst_eager_unprocessed_to_passive   true
% 1.61/1.79  % --inst_prop_sim_given                 true
% 1.61/1.79  % --inst_prop_sim_new                   false
% 1.61/1.79  % --inst_orphan_elimination             true
% 1.61/1.79  % --inst_learning_loop_flag             true
% 1.61/1.79  % --inst_learning_start                 3000
% 1.61/1.79  % --inst_learning_factor                2
% 1.61/1.79  % --inst_start_prop_sim_after_learn     3
% 1.61/1.79  % --inst_sel_renew                      solver
% 1.61/1.79  % --inst_lit_activity_flag              true
% 1.61/1.79  % --inst_out_proof                      true
% 1.61/1.79  
% 1.61/1.79  % ------ Resolution Options
% 1.61/1.79  
% 1.61/1.79  % --resolution_flag                     true
% 1.61/1.79  % --res_lit_sel                         kbo_max
% 1.61/1.79  % --res_to_prop_solver                  none
% 1.61/1.79  % --res_prop_simpl_new                  false
% 1.61/1.79  % --res_prop_simpl_given                false
% 1.61/1.79  % --res_passive_queue_type              priority_queues
% 1.61/1.79  % --res_passive_queues                  [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 1.61/1.79  % --res_passive_queues_freq             [15;5]
% 1.61/1.79  % --res_forward_subs                    full
% 1.61/1.79  % --res_backward_subs                   full
% 1.61/1.79  % --res_forward_subs_resolution         true
% 1.61/1.79  % --res_backward_subs_resolution        true
% 1.61/1.79  % --res_orphan_elimination              false
% 1.61/1.79  % --res_time_limit                      1000.
% 1.61/1.79  % --res_out_proof                       true
% 1.61/1.79  % --proof_out_file                      /export/starexec/sandbox/tmp/iprover_proof_43c944.s
% 1.61/1.79  % --modulo                              true
% 1.61/1.79  
% 1.61/1.79  % ------ Combination Options
% 1.61/1.79  
% 1.61/1.79  % --comb_res_mult                       1000
% 1.61/1.79  % --comb_inst_mult                      300
% 1.61/1.79  % ------ 
% 1.61/1.79  
% 1.61/1.79  % ------ Parsing...% successful
% 1.61/1.79  
% 1.61/1.79  % 
% 1.61/1.79  
% 1.61/1.79  
% 1.61/1.79  % ------                             Statistics
% 1.61/1.79  
% 1.61/1.79  % ------ General
% 1.61/1.79  
% 1.61/1.79  % num_of_input_clauses:                 2812
% 1.61/1.79  % num_of_input_neg_conjectures:         1
% 1.61/1.79  % num_of_splits:                        0
% 1.61/1.79  % num_of_split_atoms:                   0
% 1.61/1.79  % num_of_sem_filtered_clauses:          0
% 1.61/1.79  % num_of_subtypes:                      0
% 1.61/1.79  % monotx_restored_types:                0
% 1.61/1.79  % sat_num_of_epr_types:                 0
% 1.61/1.79  % sat_num_of_non_cyclic_types:          0
% 1.61/1.79  % sat_guarded_non_collapsed_types:      0
% 1.61/1.79  % is_epr:                               0
% 1.61/1.79  % is_horn:                              0
% 1.61/1.79  % has_eq:                               0
% 1.61/1.79  % num_pure_diseq_elim:                  0
% 1.61/1.79  % simp_replaced_by:                     0
% 1.61/1.79  % res_preprocessed:                     0
% 1.61/1.79  % prep_upred:                           0
% 1.61/1.79  % prep_unflattend:                      0
% 1.61/1.79  % pred_elim_cands:                      0
% 1.61/1.79  % pred_elim:                            0
% 1.61/1.79  % pred_elim_cl:                         0
% 1.61/1.79  % pred_elim_cycles:                     0
% 1.61/1.79  % forced_gc_time:                       0
% 1.61/1.79  % gc_basic_clause_elim:                 0
% 1.61/1.79  % parsing_time:                         0.349
% 1.61/1.79  % sem_filter_time:                      0.
% 1.61/1.79  % pred_elim_time:                       0.
% 1.61/1.79  % out_proof_time:                       0.001
% 1.61/1.79  % monotx_time:                          0.
% 1.61/1.79  % subtype_inf_time:                     0.
% 1.61/1.79  % unif_index_cands_time:                0.
% 1.61/1.80  % unif_index_add_time:                  0.
% 1.61/1.80  % total_time:                           0.413
% 1.61/1.80  % num_of_symbols:                       222
% 1.61/1.80  % num_of_terms:                         6379
% 1.61/1.80  
% 1.61/1.80  % ------ Propositional Solver
% 1.61/1.80  
% 1.61/1.80  % prop_solver_calls:                    0
% 1.61/1.80  % prop_fast_solver_calls:               0
% 1.61/1.80  % prop_num_of_clauses:                  1459
% 1.61/1.80  % prop_preprocess_simplified:           3830
% 1.61/1.80  % prop_fo_subsumed:                     0
% 1.61/1.80  % prop_solver_time:                     0.
% 1.61/1.80  % prop_fast_solver_time:                0.
% 1.61/1.80  % prop_unsat_core_time:                 0.
% 1.61/1.80  
% 1.61/1.80  % ------ QBF 
% 1.61/1.80  
% 1.61/1.80  % qbf_q_res:                            0
% 1.61/1.80  % qbf_num_tautologies:                  0
% 1.61/1.80  % qbf_prep_cycles:                      0
% 1.61/1.80  
% 1.61/1.80  % ------ BMC1
% 1.61/1.80  
% 1.61/1.80  % bmc1_current_bound:                   -1
% 1.61/1.80  % bmc1_last_solved_bound:               -1
% 1.61/1.80  % bmc1_unsat_core_size:                 -1
% 1.61/1.80  % bmc1_unsat_core_parents_size:         -1
% 1.61/1.80  % bmc1_merge_next_fun:                  0
% 1.61/1.80  % bmc1_unsat_core_clauses_time:         0.
% 1.61/1.80  
% 1.61/1.80  % ------ Instantiation
% 1.61/1.80  
% 1.61/1.80  % inst_num_of_clauses:                  undef
% 1.61/1.80  % inst_num_in_passive:                  undef
% 1.61/1.80  % inst_num_in_active:                   0
% 1.61/1.80  % inst_num_in_unprocessed:              0
% 1.61/1.80  % inst_num_of_loops:                    0
% 1.61/1.80  % inst_num_of_learning_restarts:        0
% 1.61/1.80  % inst_num_moves_active_passive:        0
% 1.61/1.80  % inst_lit_activity:                    0
% 1.61/1.80  % inst_lit_activity_moves:              0
% 1.61/1.80  % inst_num_tautologies:                 0
% 1.61/1.80  % inst_num_prop_implied:                0
% 1.61/1.80  % inst_num_existing_simplified:         0
% 1.61/1.80  % inst_num_eq_res_simplified:           0
% 1.61/1.80  % inst_num_child_elim:                  0
% 1.61/1.80  % inst_num_of_dismatching_blockings:    0
% 1.61/1.80  % inst_num_of_non_proper_insts:         0
% 1.61/1.80  % inst_num_of_duplicates:               0
% 1.61/1.80  % inst_inst_num_from_inst_to_res:       0
% 1.61/1.80  % inst_dismatching_checking_time:       0.
% 1.61/1.80  
% 1.61/1.80  % ------ Resolution
% 1.61/1.80  
% 1.61/1.80  % res_num_of_clauses:                   undef
% 1.61/1.80  % res_num_in_passive:                   undef
% 1.61/1.80  % res_num_in_active:                    0
% 1.61/1.80  % res_num_of_loops:                     0
% 1.61/1.80  % res_forward_subset_subsumed:          0
% 1.61/1.80  % res_backward_subset_subsumed:         0
% 1.61/1.80  % res_forward_subsumed:                 0
% 1.61/1.80  % res_backward_subsumed:                0
% 1.61/1.80  % res_forward_subsumption_resolution:   0
% 1.61/1.80  % res_backward_subsumption_resolution:  0
% 1.61/1.80  % res_clause_to_clause_subsumption:     0
% 1.61/1.80  % res_orphan_elimination:               0
% 1.61/1.80  % res_tautology_del:                    0
% 1.61/1.80  % res_num_eq_res_simplified:            0
% 1.61/1.80  % res_num_sel_changes:                  0
% 1.61/1.80  % res_moves_from_active_to_pass:        0
% 1.61/1.80  
% 1.61/1.80  % Status Unsatisfiable
% 1.61/1.80  % SZS status Theorem
% 1.61/1.80  % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------